%I #13 Jul 11 2022 11:27:12
%S 2,1,4,2,2,1,6,3,2,1,4,2,2,1,8,4,2,1,4,2,2,1,6,3,2,1,4,2,2,1,10,5,2,1,
%T 4,2,2,1,6,3,2,1,4,2,2,1,8,4,2,1,4,2,2,1,6,3,2,1,4,2,2,1,12,6,2,1,4,2,
%U 2,1,6,3,2,1,4,2,2,1,8,4,2,1,4,2,2,1
%N Nonzero terms of A220779: exponent of highest power of 2 dividing an even sum 1^n + 2^n + ... + n^n.
%C 2-adic valuation of Sum_{k=1..n} k^n for n == 0 or 3 mod 4.
%C See references, links, formulas, and example in A220779.
%t Table[n = 2*k + Mod[k, 2]; IntegerExponent[ Sum[a^n, {a, 1, n}], 2], {k, 150}]
%o (Python)
%o from sympy import harmonic
%o def A220780(n): return (~(m:=int(harmonic(k:=(n<<1)+(n&1),-k)))&m-1).bit_length() # _Chai Wah Wu_, Jul 11 2022
%Y Cf. A001511, A031971, A220779.
%K nonn
%O 1,1
%A _Jonathan Sondow_, Dec 20 2012