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

1,2

Links

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

Example

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

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 *)

Prog

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

Crossrefs

Cf. A000005, A051801, A074312.

Sequence in context: A355709 A335071 A073143 * A074312 A061426 A190045

Adjacent sequences: A066610 A066611 A066612 * A066614 A066615 A066616

Keyword

nonn,base,changed

Author

Amarnath Murthy, Dec 24 2001

Extensions

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

Status

approved