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A087175
Number of distinct primes dividing the n-th partition number.
6
0, 1, 1, 1, 1, 1, 2, 2, 3, 3, 2, 2, 1, 2, 2, 3, 2, 3, 3, 3, 3, 3, 2, 3, 3, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 1, 3, 3, 4, 4, 4, 3, 3, 3, 3, 4, 4, 3, 3, 3, 3, 5, 3, 5, 4, 3, 3, 4, 5, 3, 5, 4, 3, 5, 2, 4, 2, 4, 3, 4, 3, 3, 3, 4, 6, 2, 1, 4, 4, 4, 2, 4, 3, 5, 2, 5, 2, 4, 3, 2, 3, 2, 2, 6, 2, 4, 7, 3, 2, 5, 3, 3
OFFSET
1,7
LINKS
Eric Weisstein's World of Mathematics, Distinct Prime Factors
Eric Weisstein's World of Mathematics, Partition Function
FORMULA
a(n) = A001221(A000041(n)).
EXAMPLE
A000041(14) = 135 = 3^3 * 5, so a(14) = 2.
A000041(97) = 133230930 = 2*3*5*7*29*131*167, so a(97)=7.
MATHEMATICA
Table[If[n==1, 0, Length[FactorInteger[PartitionsP[n]]]], {n, 1, 100}] (* Jonathan Sondow, Aug 19 2011 *)
PROG
(PARI) a(n)={omega(numbpart(n))} \\ Andrew Howroyd, Dec 28 2017
CROSSREFS
Sequence in context: A369053 A340328 A271076 * A188817 A271099 A344259
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Aug 23 2003
STATUS
approved