A259174 Numbers whose abundance is a power of 2.

12, 20, 56, 70, 88, 104, 108, 220, 368, 464, 550, 572, 650, 748, 836, 860, 952, 992, 1232, 1504, 1672, 1888, 1952, 2140, 2392, 2744, 3708, 4030, 5336, 5830, 6328, 6536, 6808, 7192, 7304, 7544, 7912, 8968, 9656, 9820, 10184, 10792, 11096, 13496, 14008

Offset: 1

Author

Robert G. Wilson v, Jun 20 2015

Keywords

• nonn
• changed

Comments

Subsequence of A005101 whose abundance is a term of A000079 except 1.

Below 35*10^8, only 236925 is odd and its abundance is 2^9.

Least terms with abundance 2^e for e = 1, 2, ... are listed in A292558.

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..482

Crossrefs

Contains as subsequences A088831, A088832, A088833, A141547, A175989, A275996, A292626.

Cf. A005101, A292558.

Programs

Mathematica

fQ[n_] := IntegerQ@ Log2[DivisorSigma[1, n] - 2 n]; Select[ Range@ 15000, fQ]

PARI

isok(n) = isprimepower(sigma(n)-2*n, &p) && (p==2); \\ Michel Marcus, Mar 25 2017