A355950 - OEIS

%I #16 Jul 22 2022 10:12:21

%S 1,4,14,81,707,8495,126145,2223364,45270095,1045270723,26982695325,

%T 769991073865,24068076196347,817782849568143,30010708874959403,

%U 1182932213483903598,49844124089150772080,2235755683827890358557,106363105981739131891399

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

%H Seiichi Manyama, <a href="/A355950/b355950.txt">Table of n, a(n) for n = 1..387</a>

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

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

%o (PARI) a(n) = sum(k=1, n, n\k*k^(k-1));

%o (PARI) a(n) = sum(k=1, n, sumdiv(k, d, d^(d-1)));

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

%o (Python)

%o 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

%Y Partial sums of A262843.

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

%Y Cf. A060946, A355887.

%K nonn

%O 1,2

%A _Seiichi Manyama_, Jul 21 2022