# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a262965 Showing 1-1 of 1 %I A262965 #21 Dec 10 2021 11:25:55 %S A262965 12,10,14,15,26,57,38,85,87,62,111,129,86,603,159,177,122,201,219,146, %T A262965 237,927,267,545,309,206,327,218,1057,1016,1359,411,278,1267,302,471, %U A262965 489,3088,519,537,362,1561,386,597,398,1687,3856,687,458,1897,717,482 %N A262965 Least number k such that k mod s = prime(n) where s is the sum of the distinct primes dividing k. %C A262965 Conjecture: a(n) exists for all n > 0. %C A262965 Many terms are numbers with two distinct prime divisors, exceptions being a(157) = 15465, a(254) = 25815, a(279) = 28695, a(303) = 31665, ... which have three prime distinct divisors, ... %H A262965 Michel Lagneau, Table of n, a(n) for n = 1..1000 %e A262965 a(5) = 26 because 26 = 2*13 => 26 mod (2+13) = 26 mod 15 = 11 = prime(5). %t A262965 Table[k=1;While[Mod[k,Plus@@First[Transpose[FactorInteger[k]]]]!=Prime[n],k++];k,{n,50}] %o A262965 (PARI) spf(k) = my(f = factor(k)); vecsum(f[,1]); %o A262965 a(n) = {k=2; while (k % spf(k) != prime(n), k++); k;} \\ _Michel Marcus_, Oct 06 2015 %o A262965 (Python) %o A262965 from sympy import prime, primefactors %o A262965 def a(n): %o A262965 k, target = 2, prime(n) %o A262965 while k%sum(primefactors(k)) != target: k += 1 %o A262965 return k %o A262965 print([a(n) for n in range(1, 53)]) # _Michael S. Branicky_, Dec 10 2021 %Y A262965 Cf. A008472. %K A262965 nonn %O A262965 1,1 %A A262965 _Michel Lagneau_, Oct 05 2015 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE