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A379239 Numbers k for which A003961(k)-sigma(k) is prime, where A003961 is fully multiplicative with a(prime(i)) = prime(i+1), and sigma is the sum of divisors function.

%I A379239 #9 Dec 23 2024 11:38:20
%S A379239 4,6,7,10,12,13,15,19,21,22,23,28,31,33,34,35,37,39,43,45,47,48,51,53,
%T A379239 55,58,61,67,73,76,77,79,82,83,84,89,95,97,103,105,109,111,112,113,
%U A379239 115,118,123,124,127,129,131,141,142,143,145,148,151,153,155,156,157,159,161,163,165,167,173,185,187,192,193,199
%N A379239 Numbers k for which A003961(k)-sigma(k) is prime, where A003961 is fully multiplicative with a(prime(i)) = prime(i+1), and sigma is the sum of divisors function.
%H A379239 Antti Karttunen, <a href="/A379239/b379239.txt">Table of n, a(n) for n = 1..20000</a>
%H A379239 <a href="/index/Pri#prime_indices">Index entries for sequences related to prime indices in the factorization of n</a>.
%H A379239 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>.
%e A379239 10 is included as A003961(10)-sigma(10) = 21-18 = 3 which is prime.
%e A379239 13 is included as A003961(13)-sigma(13) = 17-14 = 3 which is prime.
%e A379239 23 is included as A003961(23)-sigma(23) = 29-24 = 5 which is prime.
%o A379239 (PARI) is_A379239 = A379238;
%Y A379239 Cf. A000203, A003961, A286385, A379238 (characteristic function).
%Y A379239 Subsequences: A023200, A031924, A031926, A031930, A031932, A031936, A031938, etc, i.e., all primes for which the gap to the next prime is one more than some prime.
%Y A379239 Cf. also A349165.
%K A379239 nonn
%O A379239 1,1
%A A379239 _Antti Karttunen_, Dec 23 2024