Sequences

392,541 sequences

Duplicate of A024906.A024911
Duplicate of A024906.
Numbers k such that 10*k + 1 is prime.A024912
Numbers k such that 10*k + 1 is prime.
Numbers k such that 10*k - 7 is prime.A024913
Numbers k such that 10*k - 7 is prime.
Numbers k such that 10*k - 3 is prime.A024914
Numbers k such that 10*k - 3 is prime.
Number of positions in which 2n semi-queens may be placed on an 2n X 2n toroidal board, with only one semi-queen attacking another semi-queen; also, number of interval method wirings for a cryptographic rotor of size 2n.A024915
Number of positions in which 2n semi-queens may be placed on an 2n X 2n toroidal board, with only one semi-queen attacking another semi-queen; also, number of interval method wirings for a cryptographic rotor of size 2n.
a(n) = Sum_{k=1..n} k*floor(n/k); also Sum_{k=1..n} sigma(k) where sigma(n) = sum of divisors of n (A000203).A024916
a(n) = Sum_{k=1..n} k*floor(n/k); also Sum_{k=1..n} sigma(k) where sigma(n) = sum of divisors of n (A000203).
a(n) = Sum_{k=2..n} k*floor(n/k).A024917
a(n) = Sum_{k=2..n} k*floor(n/k).
Partial sums of the sequence of prime powers (A000961).A024918
Partial sums of the sequence of prime powers (A000961).
a(n) = Sum_{k=1..n} (-1)^k*k*floor(n/k).A024919
a(n) = Sum_{k=1..n} (-1)^k*k*floor(n/k).
a(n) = Sum_{k=1..n} (n-k) * floor(n/k).A024920
a(n) = Sum_{k=1..n} (n-k) * floor(n/k).
a(n) = Sum_{k=1..n} floor((n/k)*floor(n/k)).A024921
a(n) = Sum_{k=1..n} floor((n/k)*floor(n/k)).
a(n) = Sum_{k=1..n} floor((n/k) * floor((n/k) * floor(n/k))).A024922
a(n) = Sum_{k=1..n} floor((n/k) * floor((n/k) * floor(n/k))).
Partial products of the sequence of prime powers (A000961).A024923
Partial products of the sequence of prime powers (A000961).
a(n) = Sum_{k=1..n} prime(k)*floor(n/prime(k)).A024924
a(n) = Sum_{k=1..n} prime(k)*floor(n/prime(k)).
Sum of remainders of n mod prime(k), for k = 1,2,3,...,n.A024925
Sum of remainders of n mod prime(k), for k = 1,2,3,...,n.
a(n) = Sum_{k=1..n} floor(p(k)/k).A024926
a(n) = Sum_{k=1..n} floor(p(k)/k).
a(n) = Sum_{k=1..n} k*floor( prime(k)/k ).A024927
a(n) = Sum_{k=1..n} k*floor( prime(k)/k ).
a(n) = Sum_{k=1..n} floor( (n + p(k))/k ).A024928
a(n) = Sum_{k=1..n} floor( (n + p(k))/k ).
a(n) = Sum_{k = 1..n} k*floor((n + prime(k))/k).A024929
a(n) = Sum_{k = 1..n} k*floor((n + prime(k))/k).
a(n) = sum of remainders of n mod 1,3,5,...,2k-1, where k = [ (n+1)/2 ].A024930
a(n) = sum of remainders of n mod 1,3,5,...,2k-1, where k = [ (n+1)/2 ].
a(n) = sum of remainders of n mod 2,4,6,...,2k, where k = [ n/2 ].A024931
a(n) = sum of remainders of n mod 2,4,6,...,2k, where k = [ n/2 ].
a(n) = Sum_{k=1..n} k*[ (n/k)*[ n/k ] ].A024932
a(n) = Sum_{k=1..n} k*[ (n/k)*[ n/k ] ].
a(n) = Sum_{k=1..n} k*[ (n/k)*[ (n/k)*[ n/k ] ] ].A024933
a(n) = Sum_{k=1..n} k*[ (n/k)*[ (n/k)*[ n/k ] ] ].
Sum of remainders n mod p, over all primes p < n.A024934
Sum of remainders n mod p, over all primes p < n.
Duplicate of A051034.A024935
Duplicate of A051034.
a(n) = maximal length of partitions of n into distinct primes or -1 if there is no such partition.A024936
a(n) = maximal length of partitions of n into distinct primes or -1 if there is no such partition.
a(n) = number of 2's in all partitions of n into distinct primes.A024937
a(n) = number of 2's in all partitions of n into distinct primes.
Total number of parts in all partitions of n into distinct prime parts.A024938
Total number of parts in all partitions of n into distinct prime parts.
Number of partitions of n into distinct odd primes.A024939
Number of partitions of n into distinct odd primes.
Number of partitions of n into distinct triangular numbers.A024940
Number of partitions of n into distinct triangular numbers.
Number of partitions of n into distinct primes of the form 4k + 1.A024941
Number of partitions of n into distinct primes of the form 4k + 1.
Number of partitions of n into distinct primes of the form 4k + 3.A024942
Number of partitions of n into distinct primes of the form 4k + 3.
Number of partitions of n into distinct 6k+1 primes.A024943
Number of partitions of n into distinct 6k+1 primes.
Number of partitions of n into distinct 6k-1 primes.A024944
Number of partitions of n into distinct 6k-1 primes.
a(n) = Sum_{i=1..floor((n+2)/4)} a(2i-1)*a(n-2i+1), with a(1)=a(2)=1 and a(3)=2.A024945
a(n) = Sum_{i=1..floor((n+2)/4)} a(2i-1)*a(n-2i+1), with a(1)=a(2)=1 and a(3)=2.
s(n+3)/2, where s is A024945.A024946
s(n+3)/2, where s is A024945.
a(n) = Sum_{i=1..floor((n+2)/4)} a(2i-1)*a(n-2i+1), with a(1)=a(2)=1 and a(3)=3.A024947
a(n) = Sum_{i=1..floor((n+2)/4)} a(2i-1)*a(n-2i+1), with a(1)=a(2)=1 and a(3)=3.
a(n) = s(n+3)/3, where s is A024947.A024948
a(n) = s(n+3)/3, where s is A024947.
a(n) = Sum_{i=1..floor((n+2)/4)} a(2i-1)*a(n-2i+1), with a(1)=a(2)=1 and a(3)=4.A024949
a(n) = Sum_{i=1..floor((n+2)/4)} a(2i-1)*a(n-2i+1), with a(1)=a(2)=1 and a(3)=4.
a(n) = s(n+3)/4, where s is A024949.A024950
a(n) = s(n+3)/4, where s is A024949.
a(n) = Sum_{i=1..floor((n+2)/4)} a(2i-1)*a(n-2i+1), with a(1)=a(2)=1 and a(3)=5.A024951
a(n) = Sum_{i=1..floor((n+2)/4)} a(2i-1)*a(n-2i+1), with a(1)=a(2)=1 and a(3)=5.
a(n) = s(n+3)/5, where s is A024951.A024952
a(n) = s(n+3)/5, where s is A024951.
a(n) = Sum_{i=1..floor((n+2)/4)} a(2i-1)*a(n-2i+1), with a(1)=a(2)=1 and a(3)=6.A024953
a(n) = Sum_{i=1..floor((n+2)/4)} a(2i-1)*a(n-2i+1), with a(1)=a(2)=1 and a(3)=6.
a(n) = s(n+3)/6, where s is A024953.A024954
a(n) = s(n+3)/6, where s is A024953.
a(n) = Sum_{i=1..floor((n+2)/4)} a(2i-1)*a(n-2i+1), with a(1)=a(2)=1 and a(3)=7.A024955
a(n) = Sum_{i=1..floor((n+2)/4)} a(2i-1)*a(n-2i+1), with a(1)=a(2)=1 and a(3)=7.
a(n) = A024955(n+3)/7.A024956
a(n) = A024955(n+3)/7.
a(n) = Sum_{i=1..floor((n+2)/4)} a(2i-1)*a(n-2i+1), with a(1)=2 and a(2)=a(3)=1.A024957
a(n) = Sum_{i=1..floor((n+2)/4)} a(2i-1)*a(n-2i+1), with a(1)=2 and a(2)=a(3)=1.
a(n) = Sum_{i=1..floor((n+2)/4)} a(2i-1)*a(n-2i+1), with a(1)=3 and a(2)=a(3)=1.A024958
a(n) = Sum_{i=1..floor((n+2)/4)} a(2i-1)*a(n-2i+1), with a(1)=3 and a(2)=a(3)=1.
a(n) = Sum_{i=1..floor((n+2)/4)} a(2i-1)*a(n-2i+1), with a(1)=a(3)=2 and a(2)=1.A024959
a(n) = Sum_{i=1..floor((n+2)/4)} a(2i-1)*a(n-2i+1), with a(1)=a(3)=2 and a(2)=1.
s(n+3)/4, where s is A024959.A024960
s(n+3)/4, where s is A024959.