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
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 1..387
Crossrefs
Programs
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PARI
a(n) = sum(k=1, n, n\k*k^(k-1));
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PARI
a(n) = sum(k=1, n, sumdiv(k, d, d^(d-1)));
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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
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).