cp's OEIS Frontend

A277217 Numbers k for which the sum of digits of sigma(k) = the product of digits of sigma(k).

%I A277217 #37 Jul 22 2025 18:40:14
%S A277217 1,2,3,4,5,7,86,126,131,206,207,311,1123,1213,2113,4111,10921,12211,
%T A277217 16581,21121,21211,22111,39660,51558,52940,60812,61504,63548,68822,
%U A277217 81303,83409,87081,87451,89708,94523,97307,106118,108527,110387,111611,120831,160271
%N A277217 Numbers k for which the sum of digits of sigma(k) = the product of digits of sigma(k).
%C A277217 Numbers k such that A067342(k) = A277216(k).
%C A277217 Prime terms: 2, 3, 5, 7, 131, 311, 1123, 1213, 2113, 4111, 12211, ...
%C A277217 Corresponding values of sigma(a(n)): 1, 3, 4, 7, 6, 8, 132, 312, 132, 312, 312, 312, 1124, 1214, 2114, ...
%C A277217 Only 196 terms less than 35*10^8. - _Robert G. Wilson v_, Oct 07 2016
%C A277217 Alternatively, numbers k such that sigma(k) is in A034710. - _Charlie Neder_, Dec 27 2018
%H A277217 Robert G. Wilson v, <a href="/A277217/b277217.txt">Table of n, a(n) for n = 1..196</a> (first 100 terms from Jaroslav Krizek)
%e A277217 86 is a term because sigma(86) = 132; sum and product of digits of 132 = 6.
%t A277217 Select[Range@ 200000, Total@ # == Times @@ # &@ IntegerDigits@ DivisorSigma[1, #] &] (* _Michael De Vlieger_, Oct 06 2016 *)
%o A277217 (Magma) [n: n in [1..100000] | &+Intseq(SumOfDivisors(n)) eq &*Intseq(SumOfDivisors(n))];
%o A277217 (PARI) isok(n) = my(d=digits(sigma(n))); vecprod(d) == vecsum(d); \\ _Michel Marcus_, Mar 02 2019
%Y A277217 Cf. A000203, A007953, A007954, A034710.
%Y A277217 Cf. A067342 (sum of decimal digits of sigma(n)), A277216 (product of decimal digits of sigma(n)).
%K A277217 nonn,base
%O A277217 1,2
%A A277217 _Jaroslav Krizek_, Oct 05 2016