A292558 a(n) is the smallest number k such that sigma(k) - 2k = 2^n.

20, 12, 56, 550, 572, 108, 860, 952, 1232, 6328, 3708, 40540, 37072, 79288, 327260, 357112, 302000, 527296, 1764056, 6506512, 38559776, 21893248, 42257216, 167771740, 90798560, 469761208, 508198064, 490304800, 1353048560, 2951488480, 5067417200, 32648918272, 40086360272

Offset: 1

Author

XU Pingya, Sep 19 2017

Keywords

• nonn
• changed

Comments

For n > 31, a(n) > 1.724 * 10^10.

a(1) = A088831(1), a(2) = A088832(1), a(3) = A088833(1), a(4) = A141547(1), a(5) = A175989(1), a(6) = A275996(1), a(7) = A292626(1). - Max Alekseyev, Aug 27 2025

Examples

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

Links

• Max Alekseyev, Table of n, a(n) for n = 1..50

Crossrefs

Cf. A000203, A033880, A088831, A088832, A088833, A141547, A175989, A275996.

Programs

Mathematica

Table[k = 1; While[Log[2, DivisorSigma[1, k] - 2k] != n, k++]; k, {n, 30}]

PARI

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

Extensions

Terms a(32) onward from Max Alekseyev, Aug 27 2025