cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A159555 #22 Jul 25 2022 18:32:39
%S A159555 1,6,22,72,114,148,164,260,261,780,1078,1184,1266,2952,4674,21868
%N A159555 Numbers m where m^2 divides A159553(m), where A159553(m) = Sum_{k=0..m} binomial(m,k) * gcd(m,k).
%C A159555 For the purpose of this sequence, gcd(m,0) = m.
%C A159555 No other term up to 15000. - _Michel Marcus_, Sep 06 2019
%p A159555 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
%o A159555 (PARI) f(n) = sum(k=0, n, binomial(n,k) * gcd(n,k)); \\ A159553
%o A159555 isok(n) = !(f(n) % n^2); \\ _Michel Marcus_, Sep 05 2019
%Y A159555 Cf. A159458, A159553, A159554.
%K A159555 nonn,more
%O A159555 1,2
%A A159555 _Leroy Quet_, Apr 15 2009
%E A159555 Extended by _R. J. Mathar_, Apr 29 2009
%E A159555 a(14)-a(15) from _Ray Chandler_, Jun 18 2009
%E A159555 a(16) from _Jinyuan Wang_, Jul 25 2022