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

Author

Reinhard Zumkeller, Jan 29 2004

Keywords

• nonn

Comments

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

Examples

			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
		

Links

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

Programs

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

Formula

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

Extensions

Corrected by Ralf Stephan, Jul 27 2004