A275674 Numbers m for which sum of divisors of sum of divisors of m is a power of 2.

1, 2, 4, 16, 25, 50, 64, 100, 361, 1444, 1600, 4096, 5776, 9025, 36100, 65536, 102400, 262144, 1478656, 1638400, 6553600, 23658496, 36966400, 94633984, 591462400, 1073741824, 2365849600, 26843545600, 387620798464, 9690519961600, 1152921504606846976, 28823037615171174400

Offset

1,2

Links

Table of n, a(n) for n=1..32.

Formula

A051027(a(n)) = 2^k for some k.

Example

4 is in this sequence because A051027(4) = 8 = 2^3.

Mathematica

Select[Range[10^6], IntegerQ@ Log2@ Nest[DivisorSigma[1, #] &, #, 2] &] (* Michael De Vlieger, Aug 04 2016 *)

Prog

(Magma) [n: n in [1..100000] | NumberOfDivisors(2*DivisorSigma(1, DivisorSigma(1, n)))- NumberOfDivisors(DivisorSigma(1, DivisorSigma(1, n))) eq 1];
(PARI) isok(n) = (n==1) || (ispower(sigma(sigma(n)), , &s) && (s==2)); \\ Michel Marcus, Aug 05 2016
(PARI) ispow2(n)=n>>valuation(n, 2)==1
forfactored(n=1, 10^9, if(ispow2(sigma(sigma(n[2]))), print1(n[1]", "))) \\ Charles R Greathouse IV, Aug 19 2017

Crossrefs

Cf. A046528, A051027.

Sequence in context: A372898 A234639 A358000 * A225983 A298080 A292369

Adjacent sequences: A275671 A275672 A275673 * A275675 A275676 A275677

Keyword

nonn

Author

Juri-Stepan Gerasimov, Aug 04 2016

Extensions

a(22) corrected and a(23)-a(24) from Michel Marcus, Aug 05 2016

a(25)-a(27) from Charles R Greathouse IV, Aug 19 2017

a(28) from Charles R Greathouse IV, Aug 20 2017

More terms from Jinyuan Wang, Jun 18 2021

Status

approved