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A220780
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Nonzero terms of A220779: exponent of highest power of 2 dividing an even sum 1^n + 2^n + ... + n^n.
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2
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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
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OFFSET
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1,1
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COMMENTS
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2-adic valuation of Sum_{k=1..n} k^n for n == 0 or 3 mod 4.
See references, links, formulas, and example in A220779.
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LINKS
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MATHEMATICA
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Table[n = 2*k + Mod[k, 2]; IntegerExponent[ Sum[a^n, {a, 1, n}], 2], {k, 150}]
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PROG
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(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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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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