Sequences

392,541 sequences

Least odd prime divisor of prime(n) + 1, or 1 if prime(n) + 1 is a power of 2.A023511
Least odd prime divisor of prime(n) + 1, or 1 if prime(n) + 1 is a power of 2.
Exponent of 2 in prime factorization of prime(n) + 1.A023512
Exponent of 2 in prime factorization of prime(n) + 1.
a(n) = sum of distinct prime divisors of prime(n) + 1.A023513
a(n) = sum of distinct prime divisors of prime(n) + 1.
a(n) = sum of exponents in prime-power factorization of prime(n) + 1.A023514
a(n) = sum of exponents in prime-power factorization of prime(n) + 1.
a(n) = prime(n)*prime(n-1) - 1.A023515
a(n) = prime(n)*prime(n-1) - 1.
Number of distinct prime divisors of prime(n)*prime(n-1) - 1.A023516
Number of distinct prime divisors of prime(n)*prime(n-1) - 1.
Greatest prime divisor of prime(n)*prime(n-1) - 1.A023517
Greatest prime divisor of prime(n)*prime(n-1) - 1.
Greatest exponent in prime-power factorization of prime(n)*prime(n-1) - 1.A023518
Greatest exponent in prime-power factorization of prime(n)*prime(n-1) - 1.
Least odd prime divisor of prime(n)*prime(n-1) - 1, or 1 if prime(n)*prime(n-1) - 1 is a power of 2.A023519
Least odd prime divisor of prime(n)*prime(n-1) - 1, or 1 if prime(n)*prime(n-1) - 1 is a power of 2.
Exponent of 2 in prime factorization of prime(n)*prime(n-1) - 1.A023520
Exponent of 2 in prime factorization of prime(n)*prime(n-1) - 1.
Sum of distinct prime divisors of prime(n)*prime(n-1) - 1.A023521
Sum of distinct prime divisors of prime(n)*prime(n-1) - 1.
Sum of exponents in prime-power factorization of p(n)*p(n-1) - 1.A023522
Sum of exponents in prime-power factorization of p(n)*p(n-1) - 1.
a(n) = prime(n)*prime(n-1) + 1.A023523
a(n) = prime(n)*prime(n-1) + 1.
Number of distinct prime divisors of prime(n)*prime(n-1) + 1.A023524
Number of distinct prime divisors of prime(n)*prime(n-1) + 1.
Greatest prime divisor of prime(n)*prime(n-1) + 1.A023525
Greatest prime divisor of prime(n)*prime(n-1) + 1.
Greatest exponent in prime-power factorization of p(n)*p(n-1) + 1.A023526
Greatest exponent in prime-power factorization of p(n)*p(n-1) + 1.
Least odd prime divisor of p(n)*p(n-1) + 1, or 1 if p(n)*p(n-1) + 1 is a power of 2.A023527
Least odd prime divisor of p(n)*p(n-1) + 1, or 1 if p(n)*p(n-1) + 1 is a power of 2.
Exponent of 2 in prime factorization of prime(n)*prime(n-1) + 1.A023528
Exponent of 2 in prime factorization of prime(n)*prime(n-1) + 1.
Sum of distinct prime divisors of p(n)*p(n-1) + 1.A023529
Sum of distinct prime divisors of p(n)*p(n-1) + 1.
Sum of exponents in prime-power factorization of p(n)*p(n-1) + 1.A023530
Sum of exponents in prime-power factorization of p(n)*p(n-1) + 1.
a(n) = 1 if n is of the form m(m+3)/2, otherwise 0.A023531
a(n) = 1 if n is of the form m(m+3)/2, otherwise 0.
a(n) = 0 if n is of the form m*(m+3)/2, otherwise 1.A023532
a(n) = 0 if n is of the form m*(m+3)/2, otherwise 1.
a(n) = 1 if n is of the form m(m+1)(m+2)/6, and 0 otherwise.A023533
a(n) = 1 if n is of the form m(m+1)(m+2)/6, and 0 otherwise.
Numbers k such that the largest power of 2 dividing k equals 2^omega(k).A023534
Numbers k such that the largest power of 2 dividing k equals 2^omega(k).
Convolution of natural numbers with A023531.A023535
Convolution of natural numbers with A023531.
Convolution of natural numbers with A023532.A023536
Convolution of natural numbers with A023532.
a(n) = Lucas(n+4) - (3*n+7).A023537
a(n) = Lucas(n+4) - (3*n+7).
Convolution of natural numbers with (1, p(1), p(2), ... ), where p(k) is the k-th prime.A023538
Convolution of natural numbers with (1, p(1), p(2), ... ), where p(k) is the k-th prime.
Convolution of natural numbers with composite numbers.A023539
Convolution of natural numbers with composite numbers.
Expansion of 1/((1-x)(1-5x)(1-9x)(1-11x)).A023540
Expansion of 1/((1-x)(1-5x)(1-9x)(1-11x)).
Convolution of natural numbers with Beatty sequence for the golden mean A000201.A023541
Convolution of natural numbers with Beatty sequence for the golden mean A000201.
Convolution of natural numbers with Beatty sequence for tau^2 A001950.A023542
Convolution of natural numbers with Beatty sequence for tau^2 A001950.
Convolution of natural numbers with A023533.A023543
Convolution of natural numbers with A023533.
Convolution of natural numbers with A014306.A023544
Convolution of natural numbers with A014306.
Convolution of natural numbers >= 2 and natural numbers >= 3.A023545
Convolution of natural numbers >= 2 and natural numbers >= 3.
Convolution of natural numbers >= 2 and A023531.A023546
Convolution of natural numbers >= 2 and A023531.
Convolution of natural numbers >= 2 and A023532.A023547
Convolution of natural numbers >= 2 and A023532.
Convolution of natural numbers >= 2 and Fibonacci numbers.A023548
Convolution of natural numbers >= 2 and Fibonacci numbers.
Convolution of natural numbers >= 2 and Lucas numbers.A023549
Convolution of natural numbers >= 2 and Lucas numbers.
Convolution of natural numbers >= 2 and (F(2), F(3), F(4), ...).A023550
Convolution of natural numbers >= 2 and (F(2), F(3), F(4), ...).
Self-convolution of natural numbers >= 3.A023551
Self-convolution of natural numbers >= 3.
Convolution of natural numbers >= 3 and Fibonacci numbers.A023552
Convolution of natural numbers >= 3 and Fibonacci numbers.
Convolution of integers >= 3 and Lucas numbers.A023553
Convolution of integers >= 3 and Lucas numbers.
Convolution of natural numbers >= 3 and (Fib(2), Fib(3), Fib(4), ...).A023554
Convolution of natural numbers >= 3 and (Fib(2), Fib(3), Fib(4), ...).
Self-convolution of A023531.A023555
Self-convolution of A023531.
Convolution of A023531 and A023532.A023556
Convolution of A023531 and A023532.
Convolution of A023531 and Fibonacci numbers.A023557
Convolution of A023531 and Fibonacci numbers.
Convolution of A023531 and Lucas numbers.A023558
Convolution of A023531 and Lucas numbers.
Convolution of A023531 and (1, p(1), p(2), ...).A023559
Convolution of A023531 and (1, p(1), p(2), ...).
Convolution of A023531 and composite numbers (A002808).A023560
Convolution of A023531 and composite numbers (A002808).