A057159 Numbers k that divide s(k-1), where s(1) = 1, s(k) = s(k-1) + (k+1)*3^k.

4, 13, 35, 52, 95, 119, 169, 676, 11596, 57577, 159484, 276773, 360139, 1345747, 56193997, 60640957, 604170268, 807129973

Offset: 1

Author

Robert G. Wilson v, Sep 13 2000

Keywords

• nonn
• more

Comments

No other terms below 300000. - Vaclav Kotesovec, May 05 2018

{s(n)} = {1, 28, 136, 541, 1999, 7102, 24598, ...}; 4*s(n) = 3^(n+1)*(2n+1) - 23, with g.f. x*(-1-21*x+45*x^2) / ( (x-1)*(-1+3*x)^2 ). - R. J. Mathar, May 05 2018

Programs

Mathematica

seq = RecurrenceTable[{s[n] == s[n - 1] + (n + 1)*3^n, s[1] == 1}, s, {n, 1, 20000}]; Select[Range[1, Length[seq]], Divisible[seq[[# - 1]], #] &] (* Vaclav Kotesovec, May 05 2018 *)

Extensions

Minor edits by Altug Alkan, May 05 2018

a(10)-a(12) from Vaclav Kotesovec, May 05 2018

a(13)-a(14) from Chai Wah Wu, Aug 26 2021

a(15)-a(16) from Chai Wah Wu, Sep 02 2021

a(17)-a(18) from Sean A. Irvine, May 25 2022