A113761 - OEIS

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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

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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