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 A342925 a(n) = A003415(sigma(n)), where A003415 is the arithmetic derivative, and sigma is the sum of divisors of n. 26
 0, 1, 4, 1, 5, 16, 12, 8, 1, 21, 16, 32, 9, 44, 44, 1, 21, 16, 24, 41, 80, 60, 44, 92, 1, 41, 68, 92, 31, 156, 80, 51, 112, 81, 112, 20, 21, 92, 92, 123, 41, 272, 48, 124, 71, 156, 112, 128, 22, 34, 156, 77, 81, 244, 156, 244, 176, 123, 92, 332, 33, 272, 164, 1, 124, 384, 72, 165, 272, 384, 156, 119, 39, 101, 128, 188 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS Antti Karttunen, Table of n, a(n) for n = 1..16384 FORMULA a(A023194(n)) = 1. If gcd(m,n) = 1, a(m*n) = sigma(m)*A003415(sigma(n)) + sigma(n)*A003415(sigma(m)) = sigma(m)*a(n) + sigma(n)*a(m). a(n) = (A351568(n)*A351571(n)) + (A351569(n)*A351570(n)). - Antti Karttunen, Feb 23 2022 MATHEMATICA Array[If[# < 2, 0, # Total[#2/#1 & @@@ FactorInteger[#]]] &@ DivisorSigma[1, #] &, 76] (* Michael De Vlieger, Apr 08 2021 *) PROG (PARI) A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1])); A342925(n) = A003415(sigma(n)); CROSSREFS Cf. A023194 (positions of ones, which is a subsequence of prime powers, A000961). Cf. A342922, A342923, A342924, A342926, A351568, A351569, A351570, A351571. Cf. A342021 (fixed points), A343216 [positions k where a(k) < k], A343217 [a(k) >= k], A343218 [a(k) > k]. Cf. A347870 (parity of terms), A347872, A347873, A347877 (positions of odd terms), A347878 (of even terms), A343218, A343220, A344024. Sequence in context: A132379 A193955 A130746 * A125078 A087841 A194576 Adjacent sequences: A342922 A342923 A342924 * A342926 A342927 A342928 KEYWORD nonn AUTHOR Antti Karttunen, Apr 07 2021 STATUS approved

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Last modified September 10 04:25 EDT 2024. Contains 375773 sequences. (Running on oeis4.)