A091375 Numbers k with property that the number of prime factors of k (counted with repetition) exceeds the smallest prime factor of k.

8, 12, 16, 18, 20, 24, 28, 30, 32, 36, 40, 42, 44, 48, 50, 52, 54, 56, 60, 64, 66, 68, 70, 72, 76, 78, 80, 81, 84, 88, 90, 92, 96, 98, 100, 102, 104, 108, 110, 112, 114, 116, 120, 124, 126, 128, 130, 132, 135, 136, 138, 140, 144, 148, 150, 152, 154, 156, 160, 162

Offset: 1

Author

Reinhard Zumkeller, Jan 04 2004

Keywords

• nonn

Comments

A091371(a(n)) < 0: A001222(a(n))>A020639(a(n)).

Numbers of the form m*i + n*j = k*(i+j), where i and j are > 1. - Giovanni Teofilatto, Aug 29 2007

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10438

Crossrefs

Cf. A091372, A091376, A091377.

Programs

Mathematica

Select[Range@ 162, Length@ Flatten[Table[#1, {#2}] & @@@ #] > #[[1, 1]] &@ FactorInteger@ # &] (* Michael De Vlieger, Jul 06 2016 *)

PARI

is(n)=n>7 && bigomega(n) > factor(n)[1,1] \\ Charles R Greathouse IV, Jul 06 2016

PARI

bigomegaAtLeast(n,k,startAt=2)=if(k<3, return(if(k==2,n>1&&!isprime(n),k==0||n>1))); forprime(p=startAt,logint(n,k), if(n%p==0, k-=valuation(n,p);n/=p^valuation(n,p); return(bigomegaAtLeast(n,k)))); 0
is(n)=if(n%2==0,return(bigomegaAtLeast(n/2,2))); if(n%3==0,return(bigomegaAtLeast(n/3,3,3))); if(n<9,return(0)); forprime(p=5,log(n)/lambertw(log(n)), if(n%p==0, return(bigomegaAtLeast(n/p,p,p)))); 0 \\ Charles R Greathouse IV, Jul 06 2016

Extensions

Missing a(10001)-a(10424) inserted into b-file by Andrew Howroyd, Feb 25 2018

Definition clarified by N. J. A. Sloane, Jan 20 2020