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

18480, 21840, 28560, 31920, 34320, 38640, 44880, 48048, 48720, 50160, 52080, 53040, 59280, 60720, 62160, 62370, 62832, 68880, 70224, 71760, 72240, 73710, 74256, 76560, 77520, 78960, 80080, 81840, 82992, 85008, 89040, 90480, 93840, 96390, 96720, 97680, 99120

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, May 04 2011

Keywords

• nonn

Comments

That is, numbers with prime signature {1,1,1,1,4}.

Examples

			From _Petros Hadjicostas_, Oct 26 2019: (Start)
a(1) = (2^4)*3*5*7*11 = 18480;
a(2) = (2^4)*3*5*7*13 = 21840;
a(3) = (2^4)*3*5*7*17 = 28560;
a(4) = (2^4)*3*5*7*19 = 31920.
(End)
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000
• Eric Weisstein's World of Mathematics, Prime signature.
• Wikipedia, Prime signature.
• Will Nicholes, Prime Signatures
• Index to sequences related to prime signature

Crossrefs

Cf. A179672, A190107, A190108, A190109.

Programs

Mathematica

f[n_]:=Sort[Last/@FactorInteger[n]]=={1,1,1,1,4};Select[Range[150000],f]

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

Extensions

Name edited by Petros Hadjicostas, Oct 26 2019