cp's OEIS Frontend

A256642 a(n) is the smallest number k such that the digital product of sigma(k) = n in base 10, or 0 if no such number k exists.

%I A256642 #37 Jul 16 2025 20:48:04
%S A256642 19,1,6,2,3,8,5,4,7,36,111,0,61,0,30,5041,12,0,22,0,34
%N A256642 a(n) is the smallest number k such that the digital product of sigma(k) = n in base 10, or 0 if no such number k exists.
%C A256642 a(n) is the smallest number k such that A007954(A000203(k)) = n in base 10, or 0 if no such number exists.
%C A256642 If we write -1 to indicate that no solution has so far been found for n, then the present state of the sequence is as follows: 19, 1, 6, 2, 3, 8, 5, 4, 7, 36, 111, 0, 61, 0, 30, 5041, 12, 0, 22, 0, 34, -1, 0, 0, 37, -1, 0, 18, 73, 0, 28, 0, 33, 0, 0, 49, 193, 0, 0, 0, 157, 0, 129, 0, 0, 72, 0, 0, 60, -1, 128, 0, 0, 0, 42, 0, 45, 0, 0, 0, 217, 0, 0, 12800, 112, 0, 0, 0, 0, 0, 387, 0.
%C A256642 No terms found below 10^9. - _Michel Marcus_, Apr 08 2015
%C A256642 If k exists for n = 21, 25, 49, 125 or 245, it must be bigger than 10^20; if k exists for n = 343, 375, 525, 625, 675, 729 or 735, it must be bigger than 10^18. - _Jinyuan Wang_, Nov 01 2020
%C A256642 If they exist, terms a(21), a(25), a(49) are greater than 10^59. - _Max Alekseyev_, Feb 20 2024
%F A256642 If p = prime > 7 and m >= 1, then a(mp) = 0.
%o A256642 (Magma) A256642:=func<n|exists(r){k:k in[1..10000000] | &*Intseq(SumOfDivisors(k)) eq n }select r else 0>; [A256642(n):n in[0..20]];
%Y A256642 Cf. A000203, A007954, A256635.
%K A256642 nonn,base,more
%O A256642 0,1
%A A256642 _Jaroslav Krizek_, Apr 06 2015
%E A256642 Edited by _N. J. A. Sloane_, Apr 06 2015