A352256 a(n) is the least k such that A033273(k) is equal to (A033273(n*k + 1) - 1)/n where A033273(n) is the number of nonprime divisors of n.

3, 13, 5, 41, 11, 2479, 23, 73, 103, 2249, 19, 7177, 211, 691, 3089, 1289, 53263, 726493, 41, 1597, 2243, 64406, 13129, 31351, 983, 1579, 197, 43037, 1411, 38246575, 389, 3607, 15403, 61286, 709, 1638349, 3587, 16249, 3585641, 1017119, 1292839, 132347, 593, 32203, 51963

Offset: 1

Author

Juri-Stepan Gerasimov, Mar 09 2022

Keywords

• nonn

Examples

			a(2) = 13 because A033273(13) = (A033273(2*13 + 1) - 1)/2 = (A033273(27) - 1)/2 = 1.
		

Crossrefs

Cf. A000005, A001221, A033273, A350516.

Programs

Mathematica

f[n_] := DivisorSigma[0, n] - PrimeNu[n]; a[n_] := Module[{k = 2}, While[f[k] != (f[n*k + 1] - 1)/n, k++]; k]; Array[a, 29] (* Amiram Eldar, Mar 10 2022 *)

PARI

f(n) = numdiv(n) - omega(n); \\ A033273
a(n) = my(k=2); while (f(k) != (f(n*k + 1) - 1)/n, k++); k; \\ Michel Marcus, Mar 10 2022