A160810 Numbers k such that the number of partitions of k into prime divisors of k exceeds the number of distinct transpositions of prime factors of k.

18, 24, 30, 36, 40, 42, 45, 48, 50, 54, 56, 60, 63, 66, 70, 72, 75, 78, 80, 84, 88, 90, 96, 98, 99, 100, 102, 104, 105, 108, 110, 112, 114, 117, 120, 126, 130, 132, 135, 136, 138, 140, 144, 147, 150, 152, 153, 154, 156, 160, 162, 165, 168, 170, 171, 174, 175, 176

Offset: 1

Author

Juri-Stepan Gerasimov, Nov 23 2009

Keywords

• nonn

Comments

Numbers k such that A066882(k) > A168324(k).

Crossrefs

Cf. A066882, A168324.

Programs

Maple

A066882 := proc(n) gf := 1 ; for d in numtheory[divisors](n) do if isprime(d) then gf := gf/(1-x^d) ; gf := taylor(gf,x=0,n+2) ; end if; end do: coeftayl(gf,x=0,n) ; end proc:
A168324 := proc(n) if n = 1 then 0; else multn := numtheory[bigomega](n) ; multn := factorial(multn) ; for p in ifactors(n)[2] do multn := multn/factorial(op(2,p)) ; end do: multn ; end if; end proc:
for n from 1 to 300 do if A066882(n) > A168324(n) then printf("%d,\n",n) ; end if; end do: # R. J. Mathar, May 21 2010

Extensions

More terms from R. J. Mathar, May 21 2010