A113761 Numbers k such that the number of divisors of k equals both the sum and the product of digits of k in base 10.

1, 2, 22, 2114, 11222, 21122, 22211, 112116, 121116, 1111143, 1413111, 3411111, 11111128, 11111821, 11112118, 11121231, 11811112, 13111212, 18111112, 21111118, 21111181, 21121113, 23111121, 111112119, 111119211, 192111111

Offset

1,2

Comments

Intersection of A074312 and A057531.

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Example

2114 is a term since 2+1+1+4 = 2*1*1*4 = 8 and 2114 has 8 divisors, {1, 2, 7, 14, 151, 302, 1057, 2114}.

Mathematica

L={}; Do[d=IntegerDigits@n; p=Times@@d; If[p==Plus@@d && p==DivisorSigma[0, n], AppendTo[L, n]; Print[n]], {n, 1000000}]; L
lst = {}; fQ[n_] := (id = IntegerDigits@n; Plus @@ id == Times @@ id == DivisorSigma[0, n]); Do[ If[ fQ@n, AppendTo[lst, n]], {n, 2*10^8}]; lst

Crossrefs

Cf. A034710, A057531, A074312.

Sequence in context: A054948 A330124 A104149 * A319620 A054349 A182293

Adjacent sequences: A113758 A113759 A113760 * A113762 A113763 A113764

Keyword

base,nonn

Author

Giovanni Resta, Jan 18 2006

Extensions

a(13)-a(26) from Robert G. Wilson v, Jan 19 2006

Status

approved