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

1,1

Comments

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

Links

Table of n, a(n) for n=1..58.

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

Crossrefs

Cf. A066882, A168324.

Sequence in context: A243539 A076770 A105679 * A076771 A179014 A105093

Adjacent sequences: A160807 A160808 A160809 * A160811 A160812 A160813

Keyword

nonn

Author

Juri-Stepan Gerasimov, Nov 23 2009

Extensions

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

Status

approved