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A259174
Numbers whose abundance is a power of 2.
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
1,1
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 term whose abundance has an exponent, e, of two for e>0: 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, ..., .
LINKS
MATHEMATICA
fQ[n_] := IntegerQ@ Log2[DivisorSigma[1, n] - 2 n]; Select[ Range@ 15000, fQ]
PROG
(PARI) isok(n) = isprimepower(sigma(n)-2*n, &p) && (p==2); \\ Michel Marcus, Mar 25 2017
CROSSREFS
Cf. A005101.
Sequence in context: A282754 A063690 A229355 * A109788 A341361 A181701
KEYWORD
nonn
AUTHOR
Robert G. Wilson v, Jun 20 2015
STATUS
approved