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Either 4th power of a prime, or product of a prime and the square of a different prime.
7

%I #34 Feb 23 2024 07:25:59

%S 12,16,18,20,28,44,45,50,52,63,68,75,76,81,92,98,99,116,117,124,147,

%T 148,153,164,171,172,175,188,207,212,236,242,244,245,261,268,275,279,

%U 284,292,316,325,332,333,338,356,363,369,387,388,404,412,423,425,428,436

%N Either 4th power of a prime, or product of a prime and the square of a different prime.

%C Union of A030514 and A054753.

%C Numbers that equal the product of the proper divisors of their proper divisors. - _Scott R. Shannon_, Jul 04 2021

%H Hugo Pfoertner, <a href="/A080258/b080258.txt">Table of n, a(n) for n = 1..10000</a>

%F A080256(a(n)) = 5.

%F A002033(a(n)) = 8. - _Juri-Stepan Gerasimov_, Sep 26 2009

%e 81=3*3*3*3 and 50=2*5*5 are terms.

%t Module[{nn=20,p4,sdp},p4=Prime[Range[nn]]^4;sdp=#[[1]] #[[2]]^2&/@ Select[ Tuples[Prime[Range[nn]],2],#[[1]]!=#[[2]]&];Take[Join[p4,sdp]// Union,40]] (* _Harvey P. Dale_, Jan 31 2021 *)

%o (PARI) is(n)=my(f=factor(n)[,2]~); f==[4] || f==[2,1] || f==[1,2] \\ _Charles R Greathouse IV_, Oct 16 2015

%Y Cf. A007964, A058080, A001221, A001222, A002033, A006881, A030078.

%K nonn

%O 1,1

%A _Reinhard Zumkeller_, Feb 10 2003