# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a317746 Showing 1-1 of 1 %I A317746 #37 Jun 29 2024 16:57:06 %S A317746 1,1,2,1,3,1,4,1,5,1,3,6,1,7,1,2,8,1,3,9,1,10,1,11,1,4,6,12,1,13,1,7, %T A317746 14,1,3,5,15,1,16,1,17,1,6,9,18,1,19,1,5,20,1,3,7,21,1,22,1,23,1,3,8, %U A317746 12,24,1,5,25,1,13,26,1,3,9,27,1,4,28,1,29,1,6,10,15,30 %N A317746 Irregular triangle read by rows in which row n lists the divisors k of n such that k^n + n^k == 0 (mod k + n). %C A317746 Triangle read by rows in which row n lists the type-1 divisors of n. For each divisor k of n, call k a type-r divisor of n if (r*k)^n + n^(r*k) == 0 (mod r*k + n), r >= 1. %C A317746 Triangle read by rows in which row n lists the smallest types r of divisor k of n such that (r*k)^n + n^(r*k) == 0 (mod r*k + n) begins: %C A317746 1; %C A317746 1, 1; %C A317746 1, 1; %C A317746 1, 2, 1; %C A317746 1, 1; %C A317746 1, 3, 1, 1; %C A317746 1, 1; %C A317746 1, 1, 2, 1; %C A317746 1, 1, 1; %C A317746 1, 3, 2, 1; %C A317746 1, 1; %C A317746 1, 2, 3, 1, 1, 1; %C A317746 ..., where the total number of type-1 divisors of n is the sum of the number of all trivial divisors of n and a certain number of nontrivial divisors of n, namely: 1+0, 2+0, 2+0, 2+0, 2+0, 2+1, 2+0, 2+1, 2+1, 2+0, 2+0, 2+2, ... %e A317746 Triangle begins: %e A317746 1; %e A317746 1, 2; %e A317746 1, 3; %e A317746 1, 4; %e A317746 1, 5; %e A317746 1, 3, 6; %e A317746 1, 7; %e A317746 1, 2, 8; %e A317746 1, 3, 9; %e A317746 1, 10; %e A317746 1, 11; %e A317746 1, 4, 6, 12; %t A317746 a[n_] := Select[ Divisors@ n, Mod[PowerMod[#, n, # + n] + PowerMod[n, #, # + n], # + n] == 0 &]; Array[a, 30] // Flatten (* _Robert G. Wilson v_, Aug 06 2018 *) %o A317746 (Magma) [[k: k in [ 1..n] | Denominator(n/k) eq 1 and Denominator((k^n+n^k)/(k+n)) eq 1]: n in [1..30]] %Y A317746 Cf. A027750, A070824. %K A317746 nonn,tabf %O A317746 1,3 %A A317746 _Juri-Stepan Gerasimov_, Aug 06 2018 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE