A074312 Numbers k such that the product of the digits of k equals the number of divisors of k.

1, 2, 14, 22, 24, 32, 42, 116, 122, 126, 141, 211, 221, 222, 411, 512, 1114, 1118, 1128, 1132, 1141, 1144, 1218, 1222, 1242, 1314, 1332, 1411, 1611, 1612, 2111, 2114, 2132, 2214, 2232, 2312, 2511, 3114, 3211, 3212, 4116, 4131, 4312, 6112, 8211

Offset: 1

Author

Joseph L. Pe, Sep 22 2002

Keywords

• base
• easy
• nonn

Examples

			24 is a term as the product of the digits of 24 is 2*4 = 8 and the number of divisors = 8.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A057531, A066613.

Programs

Maple

with(numtheory):l := 1:a[1] := 1:for n from 2 to 10000 do d := convert(n,base,10): if(product(d[i],i=1..nops(d))=tau(n)) then l := l+1:a[l] := n:fi:od:seq(a[i],i=1..l); # Sascha Kurz

Mathematica

Select[Range[10^4], Apply[Times, IntegerDigits[ # ]] == DivisorSigma[0, # ] &]