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 A262826 a(n) = Sum_{d|n} -(-1)^d * 2^(n^2/d) * d. 1
 2, 8, 536, 64960, 33554592, 68718964352, 562949953422208, 18446744065119352832, 2417851639229258752070144, 1267650600228227149696894752768, 2658455991569831745807614120560711680, 22300745198530623141526273540526772167065600, 748288838313422294120286634350736906063837462110208, 100433627766186892221372630770688837357523572410678079422464 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS a(n) = 2^A007814(n) * 2^n * d for some odd d, where A007814(n) equals the exponent of highest power of 2 dividing n (conjecture). LINKS FORMULA L.g.f.: Sum_{n>=1} x^n/n * 2^(n^2)/(1 + 2^(n^2)*x^n). Equals the logarithmic derivative of A158096. 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 +... 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 Cf. A158096 (exp). Sequence in context: A098870 A221065 A023365 * A013554 A175923 A076985 Adjacent sequences:  A262823 A262824 A262825 * A262827 A262828 A262829 KEYWORD nonn AUTHOR Paul D. Hanna, Oct 03 2015 STATUS approved

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Last modified August 20 20:36 EDT 2018. Contains 313927 sequences. (Running on oeis4.)