Sequences

392,541 sequences

Expansion of cosh(tan(x))/exp(x).A009161
Expansion of cosh(tan(x))/exp(x).
Expansion of cosh(tan(x).exp(x)).A009162
Expansion of cosh(tan(x).exp(x)).
Expansion of e.g.f.: cosh(tan(x)*log(1+x)).A009163
Expansion of e.g.f.: cosh(tan(x)*log(1+x)).
Expansion of cosh(tan(x)*sin(x)).A009164
Expansion of cosh(tan(x)*sin(x)).
Expansion of e.g.f. cosh(tan(x)*sinh(x)) (only even powers).A009165
Expansion of e.g.f. cosh(tan(x)*sinh(x)) (only even powers).
Expansion of cosh(tan(x)*x).A009166
Expansion of cosh(tan(x)*x).
Expansion of cosh(tan(x)/cos(x)).A009167
Expansion of cosh(tan(x)/cos(x)).
Expansion of cosh(tan(x)^2).A009168
Expansion of cosh(tan(x)^2).
Expansion of cosh(tanh(log(1+x))).A009169
Expansion of cosh(tanh(log(1+x))).
Expansion of cosh(tanh(x))/exp(x).A009170
Expansion of cosh(tanh(x))/exp(x).
Expansion of cosh(tanh(x)*exp(x)).A009171
Expansion of cosh(tanh(x)*exp(x)).
Expansion of e.g.f.: cosh(tanh(x)*log(1+x)).A009172
Expansion of e.g.f.: cosh(tanh(x)*log(1+x)).
Expansion of cosh(tanh(x)*tan(x)).A009173
Expansion of cosh(tanh(x)*tan(x)).
Expansion of e.g.f.: cosh(x)*cos(log(1+x)).A009174
Expansion of e.g.f.: cosh(x)*cos(log(1+x)).
Expansion of cosh(x)*cos(sin(x)).A009175
Expansion of cosh(x)*cos(sin(x)).
Expansion of e.g.f.: cosh(x)*cos(tan(x)).A009176
Expansion of e.g.f.: cosh(x)*cos(tan(x)).
Numbers that are the hypotenuses of more than one Pythagorean triangle.A009177
Numbers that are the hypotenuses of more than one Pythagorean triangle.
Expansion of cosh(x)*cosh(log(1+x)).A009178
Expansion of cosh(x)*cosh(log(1+x)).
E.g.f. cosh(x)/(1+x).A009179
E.g.f. cosh(x)/(1+x).
Expansion of cosh(x)/cos(log(1+x)).A009180
Expansion of cosh(x)/cos(log(1+x)).
Expansion of cosh(x)/cos(sin(x)).A009181
Expansion of cosh(x)/cos(sin(x)).
Expansion of cosh(x)/cos(tan(x)).A009182
Expansion of cosh(x)/cos(tan(x)).
Expansion of e.g.f.: cosh(x)/cosh(log(1+x)).A009183
Expansion of e.g.f.: cosh(x)/cosh(log(1+x)).
Expansion of e.g.f.: cosh(x)/exp(sin(x)).A009184
Expansion of e.g.f.: cosh(x)/exp(sin(x)).
Long leg of more than one Pythagorean triangle.A009185
Long leg of more than one Pythagorean triangle.
Expansion of e.g.f.: cosh(x)/exp(tan(x)).A009186
Expansion of e.g.f.: cosh(x)/exp(tan(x)).
Expansion of cosh(x)/exp(tanh(x)).A009187
Expansion of cosh(x)/exp(tanh(x)).
Short leg of more than one Pythagorean triangle.A009188
Short leg of more than one Pythagorean triangle.
Expansion of e.g.f.: exp(cos(x)*x).A009189
Expansion of e.g.f.: exp(cos(x)*x).
"2p-twin peaks": a(n) is the least x with lpf(x) = lpf(x + 2p) = p = prime(n) and lpf(y) < p for all x < y < x + 2p, where lpf = least prime factor; a(n) = -1 if no such x exists.A009190
"2p-twin peaks": a(n) is the least x with lpf(x) = lpf(x + 2p) = p = prime(n) and lpf(y) < p for all x < y < x + 2p, where lpf = least prime factor; a(n) = -1 if no such x exists.
a(n) = gcd(n, d(n)), where d(n) is the number of divisors of n (A000005).A009191
a(n) = gcd(n, d(n)), where d(n) is the number of divisors of n (A000005).
E.g.f. exp(log(1+x)*cos(x)).A009192
E.g.f. exp(log(1+x)*cos(x)).
Expansion of e.g.f.: exp(log(1+x)*cosh(x)).A009193
Expansion of e.g.f.: exp(log(1+x)*cosh(x)).
a(n) = gcd(n, sigma(n)).A009194
a(n) = gcd(n, sigma(n)).
a(n) = gcd(n, phi(n)).A009195
a(n) = gcd(n, phi(n)).
Expansion of e.g.f. exp(log(1+x)/cos(x)).A009196
Expansion of e.g.f. exp(log(1+x)/cos(x)).
Expansion of exp(log(1+x)/cosh(x)).A009197
Expansion of exp(log(1+x)/cosh(x)).
E.g.f. exp(log(1+x)/exp(x)).A009198
E.g.f. exp(log(1+x)/exp(x)).
Expansion of e.g.f. exp(log(1+x)^2).A009199
Expansion of e.g.f. exp(log(1+x)^2).
E.g.f. exp(sin(log(1+x))).A009200
E.g.f. exp(sin(log(1+x))).
E.g.f. exp(sin(sin(x))).A009201
E.g.f. exp(sin(sin(x))).
Expansion of e.g.f.: exp(sin(sinh(x))).A009202
Expansion of e.g.f.: exp(sin(sinh(x))).
Expansion of exp(sin(tan(x))).A009203
Expansion of exp(sin(tan(x))).
Expansion of e.g.f. exp(sin(tanh(x))).A009204
Expansion of e.g.f. exp(sin(tanh(x))).
a(n) = gcd(d(n), sigma(n)).A009205
a(n) = gcd(d(n), sigma(n)).
Expansion of e.g.f.: exp(sin(x))*x.A009206
Expansion of e.g.f.: exp(sin(x))*x.
Expansion of exp(sin(x))/cos(x).A009207
Expansion of exp(sin(x))/cos(x).
Expansion of exp(sin(x))/cosh(x).A009208
Expansion of exp(sin(x))/cosh(x).
Expansion of e.g.f.: exp(sin(x))/exp(x).A009209
Expansion of e.g.f.: exp(sin(x))/exp(x).
Expansion of e.g.f.: exp(sin(x)*cos(x)).A009210
Expansion of e.g.f.: exp(sin(x)*cos(x)).