A159555 Numbers m where m^2 divides A159553(m), where A159553(m) = Sum_{k=0..m} binomial(m,k) * gcd(m,k).

1, 6, 22, 72, 114, 148, 164, 260, 261, 780, 1078, 1184, 1266, 2952, 4674, 21868

Offset

1,2

Comments

For the purpose of this sequence, gcd(m,0) = m.

No other term up to 15000. - Michel Marcus, Sep 06 2019

Links

Table of n, a(n) for n=1..16.

Maple

A159068 := proc(n) option remember; add(binomial(n, k)*gcd(k, n), k=1..n) ; end: A159553 := proc(n) option remember ; A159068(n)+n; end: isA159555 := proc(n) if A159553(n) mod ( n^2) = 0 then true; else false; fi; end: for n from 1 do if isA159555(n) then printf("%d, \n", n) ; fi; od: # R. J. Mathar, Apr 29 2009

Prog

(PARI) f(n) = sum(k=0, n, binomial(n, k) * gcd(n, k)); \\ A159553
isok(n) = !(f(n) % n^2); \\ Michel Marcus, Sep 05 2019

Crossrefs

Cf. A159458, A159553, A159554.

Sequence in context: A171495 A178706 A276779 * A032195 A217530 A111566

Adjacent sequences: A159552 A159553 A159554 * A159556 A159557 A159558

Keyword

nonn,more

Author

Leroy Quet, Apr 15 2009

Extensions

Extended by R. J. Mathar, Apr 29 2009

a(14)-a(15) from Ray Chandler, Jun 18 2009

a(16) from Jinyuan Wang, Jul 25 2022

Status

approved