A256642 - OEIS

%I #34 Feb 20 2024 13:46:02

%S 19,1,6,2,3,8,5,4,7,36,111,0,61,0,30,5041,12,0,22,0,34

%N 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 a(n) is the smallest number k such that A007954(A000203(k)) = n in base 10, or 0 if no such number exists.

%C 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 No terms found below 10^9. - _Michel Marcus_, Apr 08 2015

%C 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 If they exist, terms a(21), a(25), a(49) are greater than 10^59. - _Max Alekseyev_, Feb 20 2024

%F If p = prime > 7 and m >= 1, then a(mp) = 0.

%o (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 Cf. A000203, A007954, A256635.

%K nonn,base,more

%O 0,1

%A _Jaroslav Krizek_, Apr 06 2015

%E Edited by _N. J. A. Sloane_, Apr 06 2015