A353300 -id:A353300 - cp's OEIS frontend

A353301 Numbers k such that A004394(k)+1 is prime.

1, 2, 3, 4, 5, 7, 9, 11, 12, 18, 21, 24, 25, 28, 35, 45, 46, 50, 56, 70, 73, 76, 78, 79, 82, 89, 94, 105, 113, 116, 118, 121, 123, 124, 138, 139, 153, 157, 159, 164, 197, 201, 203, 210, 217, 253, 261, 273, 280, 283, 287, 342, 352, 356, 381, 396, 437, 450, 471

Offset: 1

Amiram Eldar, Apr 10 2022

nonn

First differs from A306587 at n=11.

			1 is a term since A004394(1)+1 = 1+1 = 2 is prime.

Amiram Eldar, Table of n, a(n) for n = 1..300

Cf. A004394, A072828, A306587, A353300, A353302.

s = {}; abm = 0; k = 0; Do[ab = DivisorSigma[-1, n]; If[ab > abm, abm = ab; k++; If[PrimeQ[n + 1], AppendTo[s, k]]], {n, 1, 10^6}]; s

A353302 Numbers k such that A004394(k)-1 and A004394(k)+1 are twin primes.

Original entry on oeis.org

3, 4, 5, 9, 11, 12, 24, 25, 76, 82, 105, 139, 217, 1370

Offset: 1

Amiram Eldar, Apr 10 2022

a(15) > 10^5, if it exists.

			3 is a term since the third superabundant number is A004394(3) = 4 and {4-1, 4+1} = {3, 5} is a twin primes pair.

Intersection of A353300 and A353301.

Cf. A001097, A004394, A068507, A321995.

s = {}; abm = 0; k = 0; Do[ab = DivisorSigma[-1, n]; If[ab > abm, abm = ab; k++; If[PrimeQ[n - 1] && PrimeQ[n + 1], AppendTo[s, k]]], {n, 1, 10^6}]; s

cp's OEIS Frontend

A353301 Numbers k such that A004394(k)+1 is prime.

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