# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a356127 Showing 1-1 of 1 %I A356127 #17 Jul 28 2022 15:20:42 %S A356127 1,7,37,305,3435,50163,873713,17651465,405072044,10405078324, %T A356127 295716748946,9211817291426,312086923883692,11424093751088836, %U A356127 449317984131957736,18896062057875064856,846136323944211829050,40192544399241524385636 %N A356127 a(n) = Sum_{k=1..n} k^k * binomial(floor(n/k)+1,2). %F A356127 a(n) = Sum_{k=1..n} k * Sum_{d|k} d^(d-1). %F A356127 G.f.: (1/(1-x)) * Sum_{k>=1} (k * x)^k/(1 - x^k)^2. %t A356127 a[n_] := Sum[k^k * Binomial[Floor[n/k] + 1, 2], {k, 1, n}]; Array[a, 18] (* _Amiram Eldar_, Jul 28 2022*) %o A356127 (PARI) a(n) = sum(k=1, n, k^k*binomial(n\k+1, 2)); %o A356127 (PARI) a(n) = sum(k=1, n, k*sumdiv(k, d, d^(d-1))); %o A356127 (PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=1, N, (k*x)^k/(1-x^k)^2)/(1-x)) %Y A356127 Cf. A355887, A355950. %K A356127 nonn %O A356127 1,2 %A A356127 _Seiichi Manyama_, Jul 27 2022 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE