login
A190110
Numbers with prime factorization p*q*r*s*t^4 (where p, q, r, s, t are distinct primes).
5
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
Eric Weisstein's World of Mathematics, Prime signature.
Wikipedia, Prime signature.
Will Nicholes, Prime Signatures
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
KEYWORD
nonn
AUTHOR
EXTENSIONS
Name edited by Petros Hadjicostas, Oct 26 2019
STATUS
approved