A069827 Numbers k such that sigma(core(k)) = tau(k) where core(k) is the squarefree part of k, tau(k) is the number of divisors of k, and sigma(k) is their sum.

1, 20, 27, 45, 96, 150, 245, 294, 486, 504, 540, 605, 612, 726, 832, 845, 1014, 1400, 1445, 1500, 1700, 1734, 1805, 2166, 2645, 3125, 3168, 3174, 3332, 3825, 4176, 4205, 4352, 4805, 4950, 5046, 5324, 5766, 6174, 6615, 6776, 6845, 7497, 8214, 8228, 8405

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Mathematica

core[n_] := Times @@ Power @@@ ({#[[1]], Mod[ #[[2]], 2]} & /@ FactorInteger[n]); Select[Range[10^5], DivisorSigma[0, #] == DivisorSigma[1, core[#]] &] (* Amiram Eldar, Jul 11 2019 after Zak Seidov at A007913 *)

Prog

(PARI) isok(n) = sigma(core(n)) == numdiv(n); \\ Michel Marcus, Aug 09 2013

Crossrefs

Cf. A000005, A000203, A007913.

Sequence in context: A248787 A070717 A114813 * A194674 A059617 A122146

Adjacent sequences: A069824 A069825 A069826 * A069828 A069829 A069830

Keyword

easy,nonn

Author

Benoit Cloitre, Apr 28 2002

Status

approved