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

1,1

Comments

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

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

Example

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)

Mathematica

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

Prog

(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

Crossrefs

Cf. A179672, A190107, A190108, A190109.

Sequence in context: A251874 A035924 A209895 * A157738 A247205 A173274

Adjacent sequences: A190107 A190108 A190109 * A190111 A190112 A190113

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, May 04 2011

Extensions

Name edited by Petros Hadjicostas, Oct 26 2019

Status

approved