A091690 Smallest integer m such that the n-th prime A000040(n) divides partition number A000041(m).

2, 3, 4, 5, 6, 28, 54, 20, 32, 26, 44, 86, 35, 27, 56, 52, 54, 115, 47, 43, 46, 123, 29, 25, 44, 13, 78, 96, 320, 63, 40, 73, 66, 60, 333, 203, 116, 960, 22, 79, 368, 310, 75, 41, 118, 59, 100, 64, 55, 115, 316, 353, 46, 23, 197, 236, 193, 871, 179, 37, 95, 183, 233

Offset

1,1

Comments

See A091689 for comment, links and example: A091689(n) = A000041(a(n)).

Links

David A. Corneth, Table of n, a(n) for n = 1..10000 (first 2262 terms from M. F. Hasler)

Formula

a(n) = A046641(A000040(n)). - M. F. Hasler, Oct 20 2008

Example

a(10) = 26 as the 10th prime divides the 26th partition number, i.e., prime(10) = 29 | 2436 = A000041(26) and no smaller partition number is a multiple of 29. - David A. Corneth, Jan 05 2023

Prog

(PARI) forprime(p=2, 400, n=2:while(numbpart(n)%p, n=n+1):print1(n", "))
(PARI) first(n) = { my(res = vector(n, i, oo), todo = [1..n], pr = Set(primes(n)), prmap = Map()); for(i = 1, n, mapput(prmap, pr[i], todo[i]) ); for(i = 1, oo, c = numbpart(i); j = 1; while(j <= #pr && pr[j] <= c, if(c % pr[j] == 0, res[mapget(prmap, pr[j])] = i; pr = setminus(pr, Set(pr[j])); ); j++ ); if(#pr == 0, return(res) ) ); res } \\ David A. Corneth, Jan 05 2023
(sh) i=2; c=1; while [ $i -le 20000 ]; do if [ `factor $i | wc -w` = 2 ]; then awk '/^'$i' / {print "'$c' " $2; exit}' b046641.txt; let c+=1; if [ $i = 2 ]; then i=1; fi; fi; let i+=2; done # M. F. Hasler, Oct 20 2008

Crossrefs

Sequence in context: A246908 A303367 A037332 * A024640 A037403 A037439

Adjacent sequences: A091687 A091688 A091689 * A091691 A091692 A091693

Keyword

nonn

Author

Reinhard Zumkeller, Jan 29 2004

Extensions

Corrected by Ralf Stephan, Jul 27 2004

Status

approved