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A280258
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a(n) = Sum_{d|n} pxi(d), where pxi(m) is the product of totatives of m (A001783).
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3
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1, 2, 3, 5, 25, 9, 721, 110, 2243, 215, 3628801, 397, 479001601, 20027, 896923, 2027135, 20922789888001, 87334, 6402373705728001, 8729939, 47297536723, 1253566127, 1124000727777607680001, 37182647, 41363226782215962649, 608621584727, 1524503639859202243
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OFFSET
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1,2
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COMMENTS
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Conjecture: a(n) is odd for numbers in A183300; a(n) is even for numbers in A001105 (2*n^2).
Numbers n such that a(n) is prime: 2, 3, 4, 9, 12, 20, 27, ... (there are no other terms < 742). Corresponding values of primes: 2, 3, 5, 2243, 397, 8729939, 1524503639859202243, ...
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LINKS
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FORMULA
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EXAMPLE
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For n=6; sets of totatives of divisors of 6: {1}, {1}, {1, 2}, {1, 5}; a(6) = 1+1+(1*2)+(1*5) = 9.
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MATHEMATICA
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Table[Sum[Times @@ Select[Range@ d, CoprimeQ[#, d] &], {d, Divisors@ n}], {n, 27}] (* Michael De Vlieger, Jan 01 2017 *)
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PROG
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(Magma) [&+[&*[h: h in [1..d] | GCD(h, d) eq 1]: d in Divisors(n)]: n in [1..100]]
(PARI) a(n) = sumdiv(n, d, prod(k=1, d, if (gcd(k, d)==1, k, 1))); \\ Michel Marcus, Jan 02 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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STATUS
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approved
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