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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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%I #14 Aug 28 2019 03:56:46

%S 98,101,103,107,109,307,329,401,409,503,509,601,607,701,709,809,907,

%T 1009,1013,1019,1021,1031,1033,1039,1049,1051,1061,1063,1069,1087,

%U 1091,1093,1097,1103,1109,1201,1301,1303,1307,1409,1601,1607,1609,1709,1801,1901

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

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

%C 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,...

%H Amiram Eldar, <a href="/A273460/b273460.txt">Table of n, a(n) for n = 1..10000</a>

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

%p with(numtheory):

%p for n from 1 to 3000 do:

%p q:=convert(n,base,10):n0:=nops(q):

%p pr:=product('q[i]', 'i'=1..n0):p:=sigma(n)-n-1:

%p if p=pr

%p then

%p printf(`%d, `,n):

%p else

%p fi:

%p od:

%t Do[If[DivisorSigma[1, n]-n-1==Apply[Times, IntegerDigits[n]], Print[n]], {n, 2000}]

%t Select[Range[2,2000],Total[Most[Rest[Divisors[#]]]]==Times@@ IntegerDigits[ #]&] (* _Harvey P. Dale_, Jul 20 2019 *)

%Y Cf. A007954, A048050, A056709, A069675.

%K nonn,base

%O 1,1

%A _Michel Lagneau_, May 23 2016