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1, 2, 3, 6, 7, 23, 19, 66, 95, 255, 187, 1059, 631, 3227, 5243, 11426, 7711, 51887, 27595, 184911, 232887, 606627, 364723, 2807935, 2405183, 8671943, 10368079, 36873651, 18512791, 167268639, 69273667, 496472226, 551130063, 1856103039
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OFFSET
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1,2
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LINKS
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EXAMPLE
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Row 6 of Pascal's triangle is 1,6,15,20,15,6,1. The greatest common divisors of n and each integer from 1 to 6 are gcd(1,6)=1, gcd(2,6)=2, gcd(3,6)=3, gcd(4,6)=2, gcd(5,6)=1, and gcd(6,6)=6. So a(6) = (1/6)*( 6*1 + 15*2 + 20*3 + 15*2 + 6*1 + 1*6) = 138/6 = 23. Note that each term of the sum in parentheses is a multiple of 6, so 138 is a multiple of 6.
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MAPLE
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MATHEMATICA
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Table[Sum[Binomial[n, k] GCD[k, n], {k, n}]/n, {n, 34}] (* Michael De Vlieger, Aug 29 2017 *)
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PROG
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(PARI) a(n) = sum(k=1, n, binomial(n, k) * gcd(k, n))/n; \\ Michel Marcus, Aug 30 2017
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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