OFFSET
1,1
COMMENTS
Equals the logarithmic derivative of A158096.
FORMULA
EXAMPLE
L.g.f.: L(x) = 2*x + 8*x^2/2 + 536*x^3/3 + 64960*x^4/4 + 33554592*x^5/5 + ...
where
L(x) = 2/(1 + 2*x)*x + 2^4/(1 + 2^4*x^2)*x^2/2 + 2^9/(1 + 2^9*x^3)*x^3/3 + 2^16/(1 + 2^16*x^4)*x^4/4 + 2^25/(1 + 2^25*x^5)*x^5/5 + ...
and
exp(L(x)) = 1 + 2*x + 6*x^2 + 188*x^3 + 16614*x^4 + 6744492*x^5 + 11466697660*x^6 + 80444371592472*x^7 + ...+ A158096(n)*x^n + ...
MATHEMATICA
a[n_] := DivisorSum[n, -(-1)^# * 2^(n^2/#) * # &]; Array[a, 14] (* Amiram Eldar, Aug 24 2023 *)
PROG
(PARI) {a(n) = n*polcoeff(sum(k=1, n, x^k/k * 2^(k^2)/(1 + 2^(k^2)*x^k +x*O(x^n))), n)}
for(n=1, 20, print1(a(n), ", "))
(PARI) {a(n) = sumdiv(n, d, -(-1)^d * 2^(n^2/d) * d)}
for(n=1, 20, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Oct 03 2015
STATUS
approved