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Product of the 4th power of a prime (A030514) and a different prime (p^4*q).
36

%I #36 Feb 09 2024 10:07:11

%S 48,80,112,162,176,208,272,304,368,405,464,496,567,592,656,688,752,

%T 848,891,944,976,1053,1072,1136,1168,1250,1264,1328,1377,1424,1539,

%U 1552,1616,1648,1712,1744,1808,1863,1875,2032,2096,2192,2224,2349,2384,2416,2511

%N Product of the 4th power of a prime (A030514) and a different prime (p^4*q).

%C Subsequence of A030628.

%H T. D. Noe, <a href="/A178739/b178739.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 a(n) ~ kn log n with k = 1/P(4) = 1/A085964 = 12.98817.... - _Charles R Greathouse IV_, Feb 23 2017

%t f[n_]:=Sort[Last/@FactorInteger[n]]=={1,4}; Select[Range[10000], f] (* _Vladimir Joseph Stephan Orlovsky_, May 03 2011 *)

%t max = 500000; A178739 = DeleteCases[Union[Table[Prime[p] Prime[q]^4 Boole[p != q], {p, PrimePi[max/16]}, {q, PrimePi[max/2]}]], 0]; Take[A178739, 50] (* _Alonso del Arte_, Aug 05 2012 *)

%o (PARI) list(lim)=my(v=List(),t);forprime(p=2,(lim\2)^(1/4), t=p^4; forprime(q=2,lim\t, if(p==q,next); listput(v,t*q))); vecsort(Vec(v)) \\ _Charles R Greathouse IV_, Jul 20 2011

%Y Cf. A065036, A030514, A030628, A085986, A085987.

%K easy,nonn

%O 1,1

%A _Will Nicholes_, Jun 08 2010