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 A263774 Sequence is defined by the condition that Sum_{d|n} a(d)^(n/d) = mu(n)^2, where mu(n) is the Möbius function. 1
 1, 0, 0, -1, 0, 0, 0, -2, -1, 0, 0, 0, 0, 0, 0, -6, 0, -2, 0, 0, 0, 0, 0, 6, -1, 0, 0, 0, 0, 0, 0, -54, 0, 0, 0, -5, 0, 0, 0, 30, 0, 0, 0, 0, 0, 0, 0, 114, -1, -2, 0, 0, 0, 6, 0, 126, 0, 0, 0, 0, 0, 0, 0, -4470, 0, 0, 0, 0, 0, 0, 0, 252, 0, 0, 0, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,8 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 FORMULA a(1) = 1. If p>2, a(p) = 0, a(p^2) = -1, a(p^n) = 0 for n>2. a(p1*p2*..*pn) = 0, a(2*p1*...*pn) = 0, a(4*p1*...*pn) = 0. If p1,...,pn are odd it appears that: a(p1^2*p2^2*...*pn^2) = (-1)^n, a(p1^k1*p2^k2*...*pn^kn) = 0, if one of k1,...,kn > 2, a(2*p1^k1*p2^k2*...*pn^kn) > 0 if one of k1,...,kn > 1. a(2^n) = A264610(n). EXAMPLE For a prime p, a(p)^1 + a(1)^p = mu(p)^2=1 => a(p) = 0. For n=6, a(1)^6 + a(2)^3 + a(3)^2 + a(6)^1 = mu(6) = 1, so 1 - 0 + 0 + a(6) = 1, so 1 + a(6) = 1, so a(6) = 0. MAPLE a := proc (n) option remember; numtheory:-mobius(n)^2-add(procname(n/d)^d, d = `minus`(numtheory:-divisors(n), {1})) end proc; a(1) := 1; La := seq(a(i), i = 1 .. 100) MATHEMATICA a[n_]:=If[n<2, 1, MoebiusMu[n]^2 - Sum[If[d==1, 0, a[n/d]^d], {d, Divisors[n]}]]; Table[a[n], {n, 100}] (* Indranil Ghosh, Mar 26 2017 *) PROG (PARI) a(n) = if (n==1, 1, moebius(n)^2- sumdiv(n, d, if (d==1, 0, a(n/d)^d))); (Haskell) a263774 1 = 1 a263774 n = foldl (-) (a008966 n) \$ zipWith (^) (map a' \$ reverse ds) ds             where a' x = if x == n then 0 else a263774 x                   ds = a027750_row n -- Reinhard Zumkeller, Dec 06 2015 CROSSREFS Cf. A008683, A264610. Cf. A008966, A027750. Sequence in context: A074079 A037858 A037876 * A161519 A286561 A068101 Adjacent sequences:  A263771 A263772 A263773 * A263775 A263776 A263777 KEYWORD sign AUTHOR Gevorg Hmayakyan, Nov 28 2015 STATUS approved

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Last modified December 13 20:27 EST 2019. Contains 329973 sequences. (Running on oeis4.)