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

Author

Jonathan Sondow, Dec 20 2012

Keywords

• nonn

Comments

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.

Crossrefs

Cf. A001511, A031971, A220779.

Programs

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