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 A356191 a(n) is the smallest exponentially odd number that is divisible by n. 12
 1, 2, 3, 8, 5, 6, 7, 8, 27, 10, 11, 24, 13, 14, 15, 32, 17, 54, 19, 40, 21, 22, 23, 24, 125, 26, 27, 56, 29, 30, 31, 32, 33, 34, 35, 216, 37, 38, 39, 40, 41, 42, 43, 88, 135, 46, 47, 96, 343, 250, 51, 104, 53, 54, 55, 56, 57, 58, 59, 120, 61, 62, 189, 128, 65 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 FORMULA Multiplicative with a(p^e) = p^e if e is odd and p^(e+1) otherwise. a(n) = n iff n is in A268335. a(n) = A064549(n)/A007913(n). a(n) = n*A336643(n). a(n) = n^2/A350390(n). From Vaclav Kotesovec, Sep 09 2023: (Start) Let f(s) = Product_{p prime} (1 - p^(6-5*s) + p^(7-5*s) + 2*p^(5-4*s) - p^(6-4*s) + p^(3-3*s) - p^(4-3*s) - 2*p^(2-2*s)). Sum_{k=1..n} a(k) ~ Pi^2 * f(2) * n^2 / 24 * (log(n) + 3*gamma - 1/2 + 12*zeta'(2)/Pi^2 + f'(2)/f(2)), where f(2) = Product_{p prime} (1 - 4/p^2 + 4/p^3 - 1/p^4) = A256392 = 0.2177787166195363783230075141194468131307977550013559376482764035236264911..., f'(2) = f(2) * Sum_{p prime} (11*p - 5) * log(p) / (p^3 + p^2 - 3*p + 1) = f(1) * 4.7165968208567630786609552448708126340725121316268495170070986645608062483... and gamma is the Euler-Mascheroni constant A001620. (End) MATHEMATICA f[p_, e_] := If[OddQ[e], p^e, p^(e + 1)]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] PROG (PARI) a(n) = {my(f=factor(n)); prod(i=1, #f~, if(f[i, 2]%2, f[i, 1]^f[i, 2], f[i, 1]^(f[i, 2]+1)))}; (PARI) for(n=1, 100, print1(direuler(p=2, n, 1/(1 - p^2*X^2) * (1 + p*X + p^3*X^2 - p^2*X^2))[n], ", ")) \\ Vaclav Kotesovec, Sep 09 2023 CROSSREFS Cf. A064549, A007913, A268335, A336643, A350390. Similar sequences: A053149, A053143, A053167, A066638, A087320, A087321, A197863, A356192, A356193, A356194. Sequence in context: A268675 A268385 A093928 * A135874 A372329 A138682 Adjacent sequences: A356188 A356189 A356190 * A356192 A356193 A356194 KEYWORD nonn,easy,mult AUTHOR Amiram Eldar, Jul 29 2022 STATUS approved

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Last modified May 26 14:50 EDT 2024. Contains 372826 sequences. (Running on oeis4.)