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 A342458 a(n) = gcd(A001615(n), A003415(n)), where A001615 is Dedekind psi, and A003415 is the arithmetic derivative of n. 5
 1, 1, 1, 2, 1, 1, 1, 12, 6, 1, 1, 8, 1, 3, 8, 8, 1, 3, 1, 12, 2, 1, 1, 4, 10, 3, 9, 16, 1, 1, 1, 16, 2, 1, 12, 12, 1, 3, 8, 4, 1, 1, 1, 24, 3, 1, 1, 16, 14, 45, 4, 28, 1, 27, 8, 4, 2, 1, 1, 4, 1, 3, 3, 96, 6, 1, 1, 36, 2, 1, 1, 12, 1, 3, 5, 40, 6, 1, 1, 16, 108, 1, 1, 4, 2, 3, 8, 4, 1, 3, 4, 48, 2, 1, 24, 16, 1, 7, 3, 20 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 LINKS Antti Karttunen, Table of n, a(n) for n = 1..16384 FORMULA a(n) = gcd(A001615(n), A003415(n)). a(n) = A003557(n) * A342459(n). a(n) = A003415(n) / A342919(n). PROG (PARI) A001615(n) = if(1==n, n, my(f=factor(n)); prod(i=1, #f~, f[i, 1]^f[i, 2] + f[i, 1]^(f[i, 2]-1))); \\ After code in A001615 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1])); A342458(n) = gcd(A001615(n), A003415(n)); CROSSREFS Cf. A001615, A003415, A003557, A342459, A342919. Cf. A301939 (gives the positions at which a(n) = A001615(n) = A003415(n)). Cf. also A175732, A342413, A342915. Sequence in context: A066017 A236938 A079834 * A256688 A029582 A067095 Adjacent sequences:  A342455 A342456 A342457 * A342459 A342460 A342461 KEYWORD nonn AUTHOR Antti Karttunen, Mar 28 2021 STATUS approved

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Last modified June 16 04:56 EDT 2021. Contains 345056 sequences. (Running on oeis4.)