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A273460
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Numbers n such that sum of the divisors of n (except 1 and n) is equal to the product of the digits of n.
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1
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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
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1,1
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COMMENTS
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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,...
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LINKS
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EXAMPLE
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sigma(98) - 98 - 1 = 171 - 98 - 1 = 72 and 8*9 = 72 so 98 is in the sequence.
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MAPLE
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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:
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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