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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
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
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
KEYWORD
easy,nonn
AUTHOR
Benoit Cloitre, Apr 28 2002
STATUS
approved