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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.

%I A273460 #14 Aug 28 2019 03:56:46
%S A273460 98,101,103,107,109,307,329,401,409,503,509,601,607,701,709,809,907,
%T A273460 1009,1013,1019,1021,1031,1033,1039,1049,1051,1061,1063,1069,1087,
%U A273460 1091,1093,1097,1103,1109,1201,1301,1303,1307,1409,1601,1607,1609,1709,1801,1901
%N 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.
%C A273460 Or numbers n such that A048050(n) = A007954(n).
%C A273460 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 A273460 Amiram Eldar, <a href="/A273460/b273460.txt">Table of n, a(n) for n = 1..10000</a>
%e A273460 sigma(98) - 98 - 1 = 171 - 98 - 1 = 72 and 8*9 = 72 so 98 is in the sequence.
%p A273460 with(numtheory):
%p A273460 for n from 1 to 3000 do:
%p A273460   q:=convert(n,base,10):n0:=nops(q):
%p A273460   pr:=product('q[i]', 'i'=1..n0):p:=sigma(n)-n-1:
%p A273460    if p=pr
%p A273460     then
%p A273460     printf(`%d, `,n):
%p A273460     else
%p A273460    fi:
%p A273460 od:
%t A273460 Do[If[DivisorSigma[1, n]-n-1==Apply[Times, IntegerDigits[n]], Print[n]], {n, 2000}]
%t A273460 Select[Range[2,2000],Total[Most[Rest[Divisors[#]]]]==Times@@ IntegerDigits[ #]&] (* _Harvey P. Dale_, Jul 20 2019 *)
%Y A273460 Cf. A007954, A048050, A056709, A069675.
%K A273460 nonn,base
%O A273460 1,1
%A A273460 _Michel Lagneau_, May 23 2016