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 A091690 Smallest integer m such that the n-th prime A000040(n) divides partition number A000041(m). 3
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified June 13 05:35 EDT 2024. Contains 373366 sequences. (Running on oeis4.)