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

Author

Michel Lagneau, May 23 2016

Keywords

• nonn
• base

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,...

Examples

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

Links

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

Crossrefs

Cf. A007954, A048050, A056709, A069675.

Programs

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 *)