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%I #13 Jul 16 2021 03:25:14
%S 6,11,778,11735953
%N Numbers k such that sum of the proper divisors of k is product of digits of k.
%C All repunit primes are in the sequence. So A004022 is a subsequence of this sequence.
%C All terms beyond a(3) are coprime to 6, and of course all terms are zerofree (A052382). a(5) > 10^11. - _Charles R Greathouse IV_, Nov 03 2014
%C a(5) > 2*10^12. - _Giovanni Resta_, Aug 30 2018
%e sigma(11735953) = sigma(883*13291) = 11735953 + (13291 + 883 + 1) = 11735953 + 1*1*7*3*5*9*5*3 so 11735953 is in the sequence.
%t Do[If[DivisorSigma[1,n]-n==Apply[Times,IntegerDigits[n]],Print[n]], {n,50000000}]
%o (PARI) is(n)=my(d=digits(n),p=prod(i=1,#d,d[i])); p>0 && p+n==sigma(n) \\ _Charles R Greathouse IV_, Nov 03 2014
%Y Subsequence of A052382.
%Y Cf. A004022.
%K base,more,nice,nonn
%O 1,1
%A _Farideh Firoozbakht_, Oct 27 2008
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