A124239 a(n) = Sum_{k=1..n} Sum_{m=1..n} (2*k - 1)^m.

1, 14, 197, 3704, 90309, 2704470, 95856025, 3921108576, 181756280697, 9413656622446, 538727822713277, 33757715581666296, 2298714540642445405, 169016703698449309846, 13345320616706684277361, 1126219424250538393789824, 101160070702700567996590513, 9636001314414804672487492878

Offset: 1

Author

Alexander Adamchuk, Oct 22 2006

Keywords

• nonn

Comments

a(3) = 197 and a(11) = 538727822713277 are primes.

p divides a(p+1) for primes p > 3.

a(2*k-1) is odd. a(2*k) is even. a(2^k) is divisible by 2^(2*k - 1) for k > 0.

Numbers n such that a(n) is divisible by n are listed in A124240.

Links

• T. D. Noe, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A124240, A124241.

Cf. also A068563, A086787, A123855.

Programs

Mathematica

Table[Sum[(2k-1)^m,{k,1,n},{m,1,n}],{n,1,20}]

PARI

a(n) = sum(k=1, n, sum(m=1, n, (2*k - 1)^m)); \\ Michel Marcus, Apr 24 2022

Formula

a(n) = Sum_{k=1..n} Sum_{m=1..n} (2*k - 1)^m.

a(n) = n + Sum_{k=2..n} (2*k - 1)*((2*k - 1)^n - 1)/(2*(k - 1)).