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 A358309 a(n) = floor(n*sqrt(gamma(n))) - sigma(n), where sigma(n) = A000203(n) is the sum of the divisors of n and gamma(n) = A007947(n) is the greatest squarefree divisor of n. 2
 0, -1, 1, -2, 5, 2, 10, -4, 2, 13, 24, 1, 32, 28, 34, -9, 52, 5, 62, 21, 64, 67, 86, -2, 24, 90, 6, 48, 126, 92, 140, -18, 141, 144, 159, -3, 187, 174, 187, 36, 220, 176, 237, 122, 96, 239, 274, -7, 72, 65, 292, 167, 331, 12, 335, 89, 350, 351, 393, 160, 414, 392, 184, -37, 440, 392, 480, 270, 477, 441, 526 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS It appears that almost always sigma(n) <= n*sqrt(gamma(n)) (see A358308). REFERENCES József Sándor, Dragoslav S. Mitrinovic, and Borislav Crstici, Handbook of Number Theory I, Springer Science & Business Media, 2005, Chapter III, p. 77, section III.1.1.d. LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 MATHEMATICA a[n_] := Module[{f = FactorInteger[n], p, e}, {p, e} = Transpose[f]; Floor[n * Sqrt[Times @@ p]]- Times @@ ((p^(e+1)-1)/(p-1))]; a[1] = 0; Array[a, 100] (* Amiram Eldar, Apr 25 2024 *) PROG (PARI) a(n) = {my(f = factor(n)); floor(n*sqrt(vecprod(f[, 1]))) - sigma(f); } \\ Amiram Eldar, Apr 25 2024 CROSSREFS Cf. A000203, A007947, A358308. Sequence in context: A178310 A210697 A085020 * A276609 A292591 A240760 Adjacent sequences: A358306 A358307 A358308 * A358310 A358311 A358312 KEYWORD sign AUTHOR N. J. A. Sloane, Dec 09 2022 STATUS approved

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Last modified September 13 07:00 EDT 2024. Contains 375865 sequences. (Running on oeis4.)