A355887 a(n) = Sum_{k=1..n} k^k * floor(n/k).

1, 6, 34, 295, 3421, 50109, 873653, 17651130, 405071647, 10405074777, 295716745389, 9211817240589, 312086923832843, 11424093750214407, 449317984131076935, 18896062057857406028, 846136323944194170206, 40192544399241119212807

Offset: 1

Author

Seiichi Manyama, Jul 20 2022

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..386

Crossrefs

Partial sums of A062796.

Cf. A006218, A024916, A064602, A064603, A064604, A248076, A319194.

Programs

PARI

a(n) = sum(k=1, n, n\k*k^k);

PARI

a(n) = sum(k=1, n, sumdiv(k, d, d^d));

PARI

my(N=20, x='x+O('x^N)); Vec(sum(k=1, N, (k*x)^k/(1-x^k))/(1-x))

Python

def A355887(n): return n*(1+n**(n-1))+sum(k**k*(n//k) for k in range(2,n)) if n>1 else 1 # Chai Wah Wu, Jul 21 2022

Formula

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

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