A091689 Smallest partition number with n-th prime as factor.

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

Offset

1,1

Comments

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.

Scott Ahlgren and Ken Ono, Addition and Counting: The Arithmetic of Partitions, Notices of the AMS, 48 (2001) pp. 978-984. See 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

Formula

a(n) = A000041(A091690(n)).

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.

Cf. A000041, A091690.

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