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A236938 Number of partitions of n such that the parts include all primes, without multiplicity, dividing n. 3
1, 1, 1, 1, 2, 1, 1, 1, 11, 11, 3, 1, 15, 1, 7, 15, 135, 1, 101, 1, 101, 56, 30, 1, 490, 627, 56, 1575, 490, 1, 627, 1, 5604, 490, 176, 1255, 6842, 1, 297, 1255, 10143, 1, 5604, 1, 6842, 21637, 792, 1, 63261, 53174, 63261, 6842, 21637, 1, 173525, 31185, 124754 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

a(1) = 1 because the partition [1] contains all the prime factors dividing 1, i.e., none. - Giovanni Resta, Feb 04 2014

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..10000

EXAMPLE

With n = 4, 4 = 2^2.  Since 4 - (2) = 2, and the partitions of 2 are {(2), (1,1)}, the partitions of 4 that include (2) are (2, 2) and (2, 1, 1), so a(4) = 2.

MAPLE

with(numtheory): with(combinat):

a:= n-> numbpart(n-add(f, f=factorset(n))):

seq(a(n), n=0..100);  # Alois P. Heinz, Feb 04 2014

MATHEMATICA

a[n_] := If[PrimeQ[n], 1, Block[{p = First /@ FactorInteger@n}, Length@ Select[ IntegerPartitions[n], Intersection[#, p] == p &]]]; Array[a, 30] (* Giovanni Resta, Feb 04 2014 *)

a[n_] := PartitionsP[n-Sum[f, {f, FactorInteger[n][[All, 1]]}]]; Table[ a[n], {n, 0, 100}] (* Jean-Fran├žois Alcover, Nov 11 2015, after Alois P. Heinz *)

CROSSREFS

Cf. A236937, A237125.

Sequence in context: A229243 A105688 A066017 * A079834 A256688 A029582

Adjacent sequences:  A236935 A236936 A236937 * A236939 A236940 A236941

KEYWORD

nonn

AUTHOR

J. Stauduhar, Feb 03 2014

EXTENSIONS

a(15)-a(56) from Giovanni Resta, Feb 04 2014

STATUS

approved

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Last modified August 26 05:42 EDT 2019. Contains 326329 sequences. (Running on oeis4.)