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, 2323520, 966467, 90175434980549623

Offset

1,1

Comments

Erdős conjectured that every prime divides at least one value of the partition function, see Ahlgren and Ono link.

Links

Amiram Eldar, Table of n, a(n) for n = 1..1000

Scott Ahlgren and Ken Ono, Addition and Counting: The Arithmetic of Partitions, Notices of the AMS, 48 (2001) pp. 978-984. See p. 982.

Gerard 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

For n = 10, A000040(10) = 29: a(10) = A000041(26) = 2436 = 29*7*3*2*2, as 29 does not divide smaller partition numbers.

Crossrefs

Cf. A051143, A049575, A046063.

Cf. A000041, A091690.

Sequence in context: A062888 A114835 A046483 * A046482 A046941 A116692

Adjacent sequences: A091686 A091687 A091688 * A091690 A091691 A091692

Keyword

nonn

Author

Reinhard Zumkeller, Jan 29 2004

Extensions

More terms from Amiram Eldar, May 16 2025

Status

approved