

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.


1



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
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OFFSET

1,1


COMMENTS

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



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)n1:
if p=pr
then
printf(`%d, `, n):
else
fi:
od:


MATHEMATICA

Do[If[DivisorSigma[1, n]n1==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



KEYWORD

nonn,base


AUTHOR



STATUS

approved



