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 A345001 a(n) = sigma(n) + n' - 2n, where n' is the arithmetic derivative of n (A003415) and sigma is the sum of divisors (A000203). 9
 -1, 0, -1, 3, -3, 5, -5, 11, 1, 5, -9, 20, -11, 5, 2, 31, -15, 24, -17, 26, 0, 5, -21, 56, -9, 5, 13, 32, -27, 43, -29, 79, -4, 5, -10, 79, -35, 5, -6, 78, -39, 53, -41, 44, 27, 5, -45, 140, -27, 38, -10, 50, -51, 93, -22, 100, -12, 5, -57, 140, -59, 5, 29, 191, -28, 73, -65, 62, -16, 63, -69, 207, -71, 5, 29, 68 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS Coincides with A003415 only on perfect numbers (A000396). LINKS Table of n, a(n) for n=1..76. FORMULA a(n) = A003415(n) - A033879(n) = A000203(n) + A003415(n) - 2*n. a(n) = A001065(n) + A168036(n). a(n) = A344999(n) / A048250(n) = A345049(n) / A173557(n). Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = A013661 + A136141 - 2 = 0.418090735898... . - Amiram Eldar, Dec 08 2023 MATHEMATICA A003415[n_] := If[n < 2, 0, Module[{f = FactorInteger[n]}, If[PrimeQ[n], 1, Total[n*f[[All, 2]]/f[[All, 1]]]]]]; a[n_] := DivisorSigma[1, n] + A003415[n] - 2 n; Array[a, 80] (* Jean-François Alcover, Jun 12 2021 *) PROG (PARI) A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1])); A345001(n) = (sigma(n)+A003415(n)-(2*n)); CROSSREFS Cf. A000203, A000396, A001065, A003415, A033879, A168036, A344999, A345002, A345003, A345004, A345005, A345049. Cf. also A051709, A344753 (analogous sequences). Cf. A013661, A136141. Sequence in context: A241508 A099536 A374075 * A082434 A078752 A343045 Adjacent sequences: A344998 A344999 A345000 * A345002 A345003 A345004 KEYWORD sign,easy AUTHOR Antti Karttunen, Jun 05 2021 STATUS approved

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Last modified September 18 03:51 EDT 2024. Contains 375995 sequences. (Running on oeis4.)