A235710 Composite numbers k such that sum of the proper divisors of k is a power of 10.

14, 124, 194, 1324, 1994, 13324, 133324, 1130324, 1333324, 13333324, 62496048, 133333324, 92782317392, 7453083061400, 657119364560000, 671701040192960, 199999999999999994, 1333333333333333324

Offset: 1

Author

Farideh Firoozbakht, Mar 17 2014

Keywords

• nonn
• base
• more

Comments

Composite numbers k such that reversal(sigma(k)-k) = 1.

If k is prime, then sum of the proper divisors of k is 10^0.

Terms include 2*(10^A089675(k)-3) and 4*(10^A055557(k)-7)/3 for all k >= 1.

Examples

			sigma(14)-14 = 1+2+7 = 10, sigma(124)-124 = 1+2+4+31+62 = 100.
		

Crossrefs

Cf. A000203, A004086, A055557, A089675.

Programs

Mathematica

r[n_]:=FromDigits[Reverse[IntegerDigits[n]]]; Do[If[!PrimeQ[n]&& r[DivisorSigma[1,n]-n]==1, Print[n]],{n, 200000000}]

Extensions

a(13) from Giovanni Resta, Mar 21 2014

Edited and a(14)-a(18) added by Max Alekseyev, May 24 2025