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.

4, 6, 7, 10, 12, 13, 15, 19, 21, 22, 23, 28, 31, 33, 34, 35, 37, 39, 43, 45, 47, 48, 51, 53, 55, 58, 61, 67, 73, 76, 77, 79, 82, 83, 84, 89, 95, 97, 103, 105, 109, 111, 112, 113, 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

Offset: 1

Author

Antti Karttunen, Dec 23 2024

Keywords

• nonn

Examples

			10 is included as A003961(10)-sigma(10) = 21-18 = 3 which is prime.
13 is included as A003961(13)-sigma(13) = 17-14 = 3 which is prime.
23 is included as A003961(23)-sigma(23) = 29-24 = 5 which is prime.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000
• Index entries for sequences related to prime indices in the factorization of n.
• Index entries for sequences related to sigma(n).

Crossrefs

Cf. A000203, A003961, A286385, A379238 (characteristic function).

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.

Cf. also A349165.

Programs

PARI

is_A379239 = A379238;