%I #27 Jan 27 2023 21:07:31
%S 2,3,4,5,6,28,54,20,32,26,44,86,35,27,56,52,54,115,47,43,46,123,29,25,
%T 44,13,78,96,320,63,40,73,66,60,333,203,116,960,22,79,368,310,75,41,
%U 118,59,100,64,55,115,316,353,46,23,197,236,193,871,179,37,95,183,233
%N Smallest integer m such that the n-th prime A000040(n) divides partition number A000041(m).
%C See A091689 for comment, links and example: A091689(n) = A000041(a(n)).
%H David A. Corneth, <a href="/A091690/b091690.txt">Table of n, a(n) for n = 1..10000</a> (first 2262 terms from M. F. Hasler)
%F a(n) = A046641(A000040(n)). - _M. F. Hasler_, Oct 20 2008
%e 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
%o (PARI) forprime(p=2,400,n=2:while(numbpart(n)%p,n=n+1):print1(n","))
%o (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
%o (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
%K nonn
%O 1,1
%A _Reinhard Zumkeller_, Jan 29 2004
%E Corrected by _Ralf Stephan_, Jul 27 2004