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

Author

Reinhard Zumkeller, Jan 29 2004

Keywords

• nonn

Comments

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

Examples

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

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.

Crossrefs

Cf. A051143, A049575, A046063.

Cf. A000041, A091690.

Formula

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

Extensions

More terms from Amiram Eldar, May 16 2025