A292557 a(n) is the smallest number k such that 2k - sigma(k) = 2^n.

3, 5, 22, 17, 250, 134, 262, 257, 6556, 4124, 10330, 8198, 91036, 19649, 65542, 65537, 1442716, 524294, 1363258, 4194332, 4411642, 16442342, 16866106, 22075325, 156791188, 536871032, 2160104368, 536870918, 1074187546, 2147483654, 4295862586, 19492545788

Offset: 1

Author

XU Pingya, Sep 19 2017

Keywords

• nonn

Comments

Primes of the form 2^n+1, i.e., Fermat primes (A019434) are terms of this sequence.

For n > 32, a(n) > 2 * 10^10.

Examples

			sigma(20) - 2*20 = 2^1, a(1) = 20.
sigma(108) - 2*108 = 64 = 2^6, a(6) = 108.
		

Crossrefs

Cf. A019434, A033879, A125246, A125247, A125248, A191363, A275997.

Programs

Mathematica

Table[k = 1; While[Log[2, 2k - DivisorSigma[1, k]] != n, k++]; k, {n, 31}]

PARI

a(n) = my(k=1); while(2*k - sigma(k) != 2^n, k++); k; \\ Michel Marcus, Sep 19 2017