

A091689


Smallest partition number with nth prime as factor.


1



2, 3, 5, 7, 11, 3718, 386155, 627, 8349, 2436, 75175, 34262962, 14883, 3010, 526823, 281589, 386155, 1064144451, 124754, 63261, 105558, 2552338241, 4565, 1958, 75175, 101, 12132164, 118114304, 37274405776748077, 1505499, 37338, 6185689
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OFFSET

1,1


COMMENTS

a(n) = A000041(A091690(n));
Erdos conjectured that every prime divides at least one value of the partition function, see Ahlgren, Ono  link.


LINKS

Table of n, a(n) for n=1..32.
S. Ahlgren and K. Ono, Addition and Counting: The Arithmetic of Partitions, p. 982
G. P. Michon, Table of partition function p(n) (n=0 through 4096)
Eric Weisstein's World of Mathematics, Partition Function P Congruences


EXAMPLE

n=10, A000040(10)=29: a(10) = A000041(26) = 2436 =
29*7*3*2*2, as 29 doesn't divide smaller partition numbers.


CROSSREFS

Cf. A051143, A049575, A046063.
Sequence in context: A062888 A046483 A114835 * A046482 A046941 A116692
Adjacent sequences: A091686 A091687 A091688 * A091690 A091691 A091692


KEYWORD

nonn


AUTHOR

Reinhard Zumkeller, Jan 29 2004


STATUS

approved



