A273460 Numbers n such that sum of the divisors of n (except 1 and n) is equal to the product of the digits of n.

98, 101, 103, 107, 109, 307, 329, 401, 409, 503, 509, 601, 607, 701, 709, 809, 907, 1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097, 1103, 1109, 1201, 1301, 1303, 1307, 1409, 1601, 1607, 1609, 1709, 1801, 1901

Offset

1,1

Comments

Or numbers n such that A048050(n) = A007954(n).

Most of the terms are primes which have at least one 0 among their digits (A056709). The composite numbers of the sequence are 98, 329, 3383, 4343, 5561, 6623, 12773, 17267, 21479, 57721, 129383, 136259, 142943, 172793, 246959, 256631, 292571,...

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

sigma(98) - 98 - 1 = 171 - 98 - 1 = 72 and 8*9 = 72 so 98 is in the sequence.

Maple

with(numtheory):
for n from 1 to 3000 do:
  q:=convert(n, base, 10):n0:=nops(q):
  pr:=product('q[i]', 'i'=1..n0):p:=sigma(n)-n-1:
   if p=pr
    then
    printf(`%d, `, n):
    else
   fi:
od:

Mathematica

Do[If[DivisorSigma[1, n]-n-1==Apply[Times, IntegerDigits[n]], Print[n]], {n, 2000}]
Select[Range[2, 2000], Total[Most[Rest[Divisors[#]]]]==Times@@ IntegerDigits[ #]&] (* Harvey P. Dale, Jul 20 2019 *)

Crossrefs

Cf. A007954, A048050, A056709, A069675.

Sequence in context: A129887 A205067 A307371 * A095605 A095589 A039491

Adjacent sequences: A273457 A273458 A273459 * A273461 A273462 A273463

Keyword

nonn,base

Author

Michel Lagneau, May 23 2016

Status

approved