A270413 Numbers m such that sigma(m-1) is a prime.

3, 5, 10, 17, 26, 65, 290, 730, 1682, 2402, 3482, 4097, 5042, 7922, 10202, 15626, 17162, 27890, 28562, 29930, 65537, 83522, 85850, 146690, 262145, 279842, 458330, 491402, 531442, 552050, 579122, 597530, 683930, 703922, 707282, 734450, 829922, 1190282, 1203410

Offset: 1

Author

Jaroslav Krizek, Mar 16 2016

Keywords

• nonn

Comments

Prime terms are in A249759.

Corresponding values of sigma(n-1): 3, 7, 13, 31, 31, 127, 307, 1093, ...

Conjecture: supersequence of A256438.

Conjecture: 31 is the only prime p such that p = sigma(x-1) = sigma(y-1) for distinct numbers x and y; 31 = sigma(17-1) = sigma(26-1).

Supersequence of A270414 and A270415.

Examples

			17 is in the sequence because sigma(17-1) = sigma(16) = 31 (prime).
		

Crossrefs

Cf. A000203, A023194, A249759, A256438, A270414, A270415.

Programs

Magma

[n: n in [2..2000000] |  IsPrime(SumOfDivisors(n-1))];

Mathematica

Select[Range[10^6], PrimeQ@ DivisorSigma[1, # - 1] &] (* Michael De Vlieger, Mar 17 2016 *)

PARI

isok(n) = isprime(sigma(n-1)); \\ Michel Marcus, Mar 17 2016

Formula

a(n) = A023194(n) + 1.