cp's OEIS Frontend

A262965 Least number k such that k mod s = prime(n) where s is the sum of the distinct primes dividing k.

%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, <a href="/A262965/b262965.txt">Table of n, a(n) for n = 1..1000</a>
%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