cp's OEIS Frontend

A344746 a(n) = Sum_{k=1..n} d(k) * k^c(n/k), where c(n) = 1 - ceiling(n) + floor(n).

%I A344746 #23 Jun 02 2021 19:24:11
%S A344746 1,5,9,19,18,40,28,59,51,73,49,136,61,107,113,164,84,210,96,235,166,
%T A344746 180,120,397,167,217,227,338,159,469,173,419,275,293,287,682,214,332,
%U A344746 330,667,240,666,254,549,538,412,280,1056,357,619,447,658,323,907,475,944,507,533,365
%N A344746 a(n) = Sum_{k=1..n} d(k) * k^c(n/k), where c(n) = 1 - ceiling(n) + floor(n).
%C A344746 For 1 <= k <= n, if k|n then add k * d(k), otherwise add d(k).
%C A344746 If p is prime, a(p) = Sum_{k=1..p} d(k) * k^c(p/k) = 2*p + Sum_{k=1..p-1} d(k) = 2*p - 2 + d(p) + Sum_{k=1..p-1} d(k) = 2*p - 2 + Sum_{k=1..p} d(k).
%e A344746 a(8) = Sum_{k=1..8} d(k) * k^c(8/k) = d(1)*1^1 + d(2)*2^1 + d(3)*3^0 + d(4)*4^1 + d(5)*5^0 + d(6)*6^0 + d(7)*7^0 + d(8)*8^1 = 1*1 + 2*2 + 2*1 + 3*4 + 2*1 + 4*1 + 2*1 + 4*8 = 59.
%t A344746 Table[Sum[DivisorSigma[0, k] k^(1 - Ceiling[n/k] + Floor[n/k]), {k, n}], {n, 80}]
%Y A344746 Cf. A000005 (tau), A006218, A143127.
%K A344746 nonn
%O A344746 1,2
%A A344746 _Wesley Ivan Hurt_, Jun 02 2021