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 A099636 a(n) = gcd(sum of distinct prime factors of n, product of distinct prime factors of n). 7
 1, 2, 3, 2, 5, 1, 7, 2, 3, 1, 11, 1, 13, 1, 1, 2, 17, 1, 19, 1, 1, 1, 23, 1, 5, 1, 3, 1, 29, 10, 31, 2, 1, 1, 1, 1, 37, 1, 1, 1, 41, 6, 43, 1, 1, 1, 47, 1, 7, 1, 1, 1, 53, 1, 1, 1, 1, 1, 59, 10, 61, 1, 1, 2, 1, 2, 67, 1, 1, 14, 71, 1, 73, 1, 1, 1, 1, 6, 79, 1, 3, 1, 83, 6, 1, 1, 1, 1, 89, 10, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Antti Karttunen, Table of n, a(n) for n = 1..20000 FORMULA From Antti Karttunen, Feb 01 2021: (Start) a(n) = gcd(A007947(n), A008472(n)). a(n) = A007947(n) / A340677(n) = A008472(n) / A340678(n). (End) EXAMPLE n=84: a(84) = gcd(2*3*7, 2+3+7) = gcd(42, 12) = 6. MATHEMATICA PrimeFactors[n_Integer] := Flatten[ Table[ # [[1]], {1}] & /@ FactorInteger[n]]; f[n_] := Block[{pf = PrimeFactors[n]}, GCD[Plus @@ pf, Times @@ pf]]; Table[ f[n], {n, 93}] (* Robert G. Wilson v, Nov 04 2004 *) PROG (PARI) A007947(n) = factorback(factorint(n)[, 1]); \\ From A007947 A008472(n) = vecsum(factor(n)[, 1]); \\ From A008472 A099636(n) = gcd(A007947(n), A008472(n)); CROSSREFS Cf. A007947, A008472, A082299, A099634, A340677, A340678. Differs from related A099635 for the first time at n=84, where a(84) = 6, while A099635(84) = 12. Differs from A014963 for the first time at n=30, where a(30) = 10, while A014963(30) = 1. Sequence in context: A157753 A020500 A014963 * A099635 A178380 A178375 Adjacent sequences: A099633 A099634 A099635 * A099637 A099638 A099639 KEYWORD nonn AUTHOR Labos Elemer, Oct 28 2004 EXTENSIONS Name clarified by Antti Karttunen, Feb 01 2021 STATUS approved

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Last modified February 24 11:15 EST 2024. Contains 370303 sequences. (Running on oeis4.)