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 A091689 Smallest partition number with n-th 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified June 14 12:37 EDT 2024. Contains 373400 sequences. (Running on oeis4.)