A007624 Numbers m such that the product of proper divisors of m = m^k, k>1. (Formerly M4824)

12, 18, 20, 24, 28, 30, 32, 40, 42, 44, 45, 48, 50, 52, 54, 56, 60, 63, 66, 68, 70, 72, 75, 76, 78, 80, 84, 88, 90, 92, 96, 98, 99, 102, 104, 105, 108, 110, 112, 114, 116, 117, 120, 124, 126, 128, 130, 132, 135, 136, 138, 140, 147, 148, 150, 152, 153, 154

Offset

1,1

References

A. H. Beiler, Recreations in the Theory of Numbers, Dover, NY, 1964, p. 23.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

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

Formula

d(n) > 4 and even.

a(n) = n + O(n/log n). - Charles R Greathouse IV, Oct 23 2015

Mathematica

ppdQ[n_]:=Module[{c=Log[n, Times@@Most[Divisors[n]]]}, c>1&&IntegerQ[c]]; Select[Range[2, 160], ppdQ] (* Harvey P. Dale, Mar 06 2012 *)
Select[Range[154], EvenQ[(d = DivisorSigma[0, #])] && d > 4 &] (* Amiram Eldar, Nov 20 2019 *)

Crossrefs

Cf. A000005, A007956.

Sequence in context: A319229 A334160 A271345 * A036456 A102467 A342973

Adjacent sequences: A007621 A007622 A007623 * A007625 A007626 A007627

Keyword

nonn,easy

Author

N. J. A. Sloane, Robert G. Wilson v, Mira Bernstein

Status

approved