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

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

Author

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

Keywords

• nonn
• easy

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

Crossrefs

Cf. A000005, A007956.

Programs

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 *)

Formula

d(n) > 4 and even.

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