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A383228 a(n) is the number of cases where both j and k (1 <= j < k <= n), are divisors of Sum_{i=j..k} i^i.

%I A383228 #20 Apr 22 2025 07:49:18
%S A383228 0,0,0,1,1,2,2,2,3,3,3,3,3,3,4,4,5,5,6,6,6,6,6,6,6,7,7,7,7,8,8,8,8,8,
%T A383228 8,8,8,8,8,8,8,9,9,10,11,11,11,11,12,12,12,12,12,12,12,14,14,14,14,15,
%U A383228 15,15,16,16,16,16,16,16,16,17,17,17,17,17,17,17,17,17,17,17
%N A383228 a(n) is the number of cases where both j and k (1 <= j < k <= n), are divisors of Sum_{i=j..k} i^i.
%H A383228 Jean-Marc Rebert, <a href="/A383228/b383228.txt">Table of n, a(n) for n = 1..1000</a>
%e A383228 1 and 4 divide Sum_{i = 1..4} i^i = 288, and
%e A383228 1 and 17 divide Sum_{i = 1..17} i^i = 846136323944176515621, and
%e A383228 1 and 19 divide Sum_{i = 1..19} i^i = 2018612200059554303215024, and
%e A383228 2 and 9 divide Sum_{i = 2..9} i^i = 405071316, and
%e A383228 2 and 30 divide Sum_{i = 2..30} i^i = 208492413443704093346554910065262730566475780, and
%e A383228 3 and 6 divide Sum_{i = 3..6} i^i = 50064, and
%e A383228 5 and 15 divide Sum_{i = 5..15} i^i = 449317984130199540, and
%e A383228 14 and 42 divide Sum_{i = 14..42} i^i = 151474018115847331407847533862930150275321445330384244581082952733296, and
%e A383228 22 and 26 divide Sum_{i = 22..26} i^i = 6246292379849897330286605654999947328, so a(42) = 9.
%o A383228 (PARI) a(n) = sum(j=1, n, sum(k=j+1, n, my(s=sum(i=j, k, i^i)); !(s % j) && !(s % k))); \\ _Michel Marcus_, Apr 20 2025
%Y A383228 Cf. A000312, A001923, A128981.
%K A383228 nonn
%O A383228 1,6
%A A383228 _Jean-Marc Rebert_, Apr 20 2025
%E A383228 More terms from _Michel Marcus_, Apr 20 2025