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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. 0
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 7 12:58 EST 2023. Contains 360123 sequences. (Running on oeis4.)