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A190110 Numbers with prime factorization p*q*r*s*t^4 (where p, q, r, s, t are distinct primes).

%I A190110 #24 Feb 16 2025 08:33:14
%S A190110 18480,21840,28560,31920,34320,38640,44880,48048,48720,50160,52080,
%T A190110 53040,59280,60720,62160,62370,62832,68880,70224,71760,72240,73710,
%U A190110 74256,76560,77520,78960,80080,81840,82992,85008,89040,90480,93840,96390,96720,97680,99120
%N A190110 Numbers with prime factorization p*q*r*s*t^4 (where p, q, r, s, t are distinct primes).
%C A190110 That is, numbers with prime signature {1,1,1,1,4}.
%H A190110 T. D. Noe, <a href="/A190110/b190110.txt">Table of n, a(n) for n = 1..1000</a>
%H A190110 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrimeSignature.html">Prime signature</a>.
%H A190110 Wikipedia, <a href="https://en.wikipedia.org/wiki/Prime_signature">Prime signature</a>.
%H A190110 Will Nicholes, <a href="http://willnicholes.com/math/primesiglist.htm">Prime Signatures</a>
%H A190110 <a href="/index/Pri#prime_signature">Index to sequences related to prime signature</a>
%e A190110 From _Petros Hadjicostas_, Oct 26 2019: (Start)
%e A190110 a(1) = (2^4)*3*5*7*11 = 18480;
%e A190110 a(2) = (2^4)*3*5*7*13 = 21840;
%e A190110 a(3) = (2^4)*3*5*7*17 = 28560;
%e A190110 a(4) = (2^4)*3*5*7*19 = 31920.
%e A190110 (End)
%t A190110 f[n_]:=Sort[Last/@FactorInteger[n]]=={1,1,1,1,4};Select[Range[150000],f]
%o A190110 (PARI) list(lim)=my(v=List(),t1,t2,t3,t4); forprime(p1=2,sqrtnint(lim\210, 4), t1=p1^4; forprime(p2=2,lim\(30*t1), if(p2==p1, next); t2=p2*t1; forprime(p3=2,lim\(6*t2), if(p3==p1 || p3==p2, next); t3=p3*t2; forprime(p4=2,lim\(2*t3), if(p4==p1 || p4==p2 || p4==p3, next); t4=p4*t3; forprime(p5=2,lim\t4, if(p5==p1 || p5==p2 || p5==p3 || p5==p4, next); listput(v, t4*p5)))))); Set(v) \\ _Charles R Greathouse IV_, Aug 25 2016
%Y A190110 Cf. A179672, A190107, A190108, A190109.
%K A190110 nonn
%O A190110 1,1
%A A190110 _Vladimir Joseph Stephan Orlovsky_, May 04 2011
%E A190110 Name edited by _Petros Hadjicostas_, Oct 26 2019