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A007624 Numbers m such that the product of proper divisors of m = m^k, k>1.
(Formerly M4824)
4

%I M4824

%S 12,18,20,24,28,30,32,40,42,44,45,48,50,52,54,56,60,63,66,68,70,72,75,

%T 76,78,80,84,88,90,92,96,98,99,102,104,105,108,110,112,114,116,117,

%U 120,124,126,128,130,132,135,136,138,140,147,148,150,152,153,154

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

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

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

%H Amiram Eldar, <a href="/A007624/b007624.txt">Table of n, a(n) for n = 1..10000</a>

%F d(n) > 4 and even.

%F a(n) = n + O(n/log n). - _Charles R Greathouse IV_, Oct 23 2015

%t 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 *)

%t Select[Range[154], EvenQ[(d = DivisorSigma[0,#])] && d > 4 &] (* _Amiram Eldar_, Nov 20 2019 *)

%Y Cf. A000005, A007956.

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_, _Robert G. Wilson v_, _Mira Bernstein_

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Last modified July 6 23:01 EDT 2020. Contains 335484 sequences. (Running on oeis4.)