A355950 a(n) = Sum_{k=1..n} k^(k-1) * floor(n/k).

1, 4, 14, 81, 707, 8495, 126145, 2223364, 45270095, 1045270723, 26982695325, 769991073865, 24068076196347, 817782849568143, 30010708874959403, 1182932213483903598, 49844124089150772080, 2235755683827890358557, 106363105981739131891399

Offset

1,2

Links

Seiichi Manyama, Table of n, a(n) for n = 1..387

Formula

a(n) = Sum_{k=1..n} Sum_{d|k} d^(d-1).

G.f.: (1/(1-x)) * Sum_{k>0} k^(k-1) * x^k/(1 - x^k).

Prog

(PARI) a(n) = sum(k=1, n, n\k*k^(k-1));
(PARI) a(n) = sum(k=1, n, sumdiv(k, d, d^(d-1)));
(PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=1, N, k^(k-1)*x^k/(1-x^k))/(1-x))
(Python)
def A355950(n): return n*(1+n**(n-2))+sum(k**(k-1)*(n//k) for k in range(2, n)) if n>1 else 1 # Chai Wah Wu, Jul 21 2022

Crossrefs

Partial sums of A262843.

Cf. A006218, A268235, A344814, A344815, A344816.

Cf. A060946, A355887.

Sequence in context: A187847 A277039 A003707 * A063862 A222497 A327355

Adjacent sequences: A355947 A355948 A355949 * A355951 A355952 A355953

Keyword

nonn

Author

Seiichi Manyama, Jul 21 2022

Status

approved