

A159555


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


0



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



