A066613 Numbers k such that the product of the nonzero digits of k equals the number of divisors of k.

1, 2, 14, 22, 24, 32, 42, 116, 122, 126, 141, 202, 211, 221, 222, 260, 280, 340, 402, 411, 440, 512, 620, 840, 1021, 1041, 1062, 1114, 1118, 1128, 1132, 1141, 1144, 1201, 1202, 1206, 1218, 1222, 1242, 1250, 1314, 1332, 1340, 1380, 1401, 1411, 1602, 1611

Offset: 1

Author

Amarnath Murthy, Dec 24 2001

Keywords

• nonn
• base

Examples

			24 is a term as there are 8 divisors of 24 = 2*4.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..10000 (first 1000 terms from Harry J. Smith)

Crossrefs

Cf. A000005, A051801, A074312.

Programs

Mathematica

f[n_] := Block[ {a = Sort[ IntegerDigits[n]] }, While[ First[a] == 0, a = Drop[a, 1]]; Return[ Apply[ Times, a]]]; Select[ Range[10^4], f[ # ] == Length[ Divisors[ # ]] & ]
pndQ[n_]:=Times@@Select[IntegerDigits[n],#!=0&]==DivisorSigma[0,n]; Select[Range[2000],pndQ] (* Harvey P. Dale, Oct 25 2016 *)

PARI

isok(k) = { vecprod(select(x->(x!=0), digits(k))) == numdiv(k) } \\ Harry J. Smith, Mar 12 2010

Extensions

Corrected and extended by Jason Earls and Robert G. Wilson v, Dec 26 2001