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%I #36 Feb 08 2024 07:12:54
%S 24,40,54,56,88,104,135,136,152,184,189,232,248,250,296,297,328,344,
%T 351,375,376,424,459,472,488,513,536,568,584,621,632,664,686,712,776,
%U 783,808,824,837,856,872,875,904,999,1016,1029,1048,1096,1107,1112
%N Product of the cube of a prime (A030078) and a different prime.
%C This sequence appears on row 8 of the list illustrated in A064839 and is similar to A054753 which appears on row 6. Previous rows are generated by A000007, A000040, A001248, A006881, A030078 respectively.
%C Or, the numbers n such that 20=number of perfect partitions of n. - _Juri-Stepan Gerasimov_, Sep 26 2009
%C A089233(a(n)) = 3. - _Reinhard Zumkeller_, Sep 04 2013
%H T. D. Noe, <a href="/A065036/b065036.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Pri#prime_signature">Index to sequences related to prime signature</a>
%F A002033(a(n)) = 20. - _Juri-Stepan Gerasimov_, Sep 26 2009
%F A000005(a(n)) = 8. - _Altug Alkan_, Nov 11 2015
%e a(4)= 56 since 56 = 2*2*2*7.
%t Select[ Range[1500], Sort[ Transpose[ FactorInteger[ # ]] [[2]]] == {1, 3} & ]
%t Module[{upto=1200},Select[(Union[Flatten[{#[[1]]^3 #[[2]],#[[1]]#[[2]]^3}&/@Subsets[Prime[Range[upto/8]],{2}]]]),#<=upto&]] (* _Harvey P. Dale_, May 23 2015 *)
%o (PARI) list(lim)=my(v=List(),t);forprime(p=2,(lim\2)^(1/3),t=p^3; forprime(q=2,lim\t,if(p==q,next);listput(v,t*q)));vecsort(Vec(v)) \\ _Charles R Greathouse IV_, Jul 20 2011
%o (PARI) is(n)=my(f=factor(n)[,2]); f==[3,1]~||f==[1,3]~ \\ _Charles R Greathouse IV_, Oct 15 2015
%Y Cf. A000007, A000040, A001248, A002033, A006881, A030078, A054753, A064839.
%K easy,nonn
%O 1,1
%A _Alford Arnold_, Nov 04 2001
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