A220780 Nonzero terms of A220779: exponent of highest power of 2 dividing an even sum 1^n + 2^n + ... + n^n.
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, 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, 2, 1, 6, 3, 2, 1, 4, 2, 2, 1, 8, 4, 2, 1, 4, 2, 2, 1
Offset: 1
Keywords
Programs
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Mathematica
Table[n = 2*k + Mod[k, 2]; IntegerExponent[ Sum[a^n, {a, 1, n}], 2], {k, 150}] -
Python
from sympy import harmonic def A220780(n): return (~(m:=int(harmonic(k:=(n<<1)+(n&1),-k)))&m-1).bit_length() # Chai Wah Wu, Jul 11 2022
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