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%I #15 Sep 08 2022 08:46:18
%S 1,2,3,5,25,9,721,110,2243,215,3628801,397,479001601,20027,896923,
%T 2027135,20922789888001,87334,6402373705728001,8729939,47297536723,
%U 1253566127,1124000727777607680001,37182647,41363226782215962649,608621584727,1524503639859202243
%N a(n) = Sum_{d|n} pxi(d), where pxi(m) is the product of totatives of m (A001783).
%C Conjecture: a(n) is odd for numbers in A183300; a(n) is even for numbers in A001105 (2*n^2).
%C 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, ...
%H Robert G. Wilson v, <a href="/A280258/b280258.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) = Sum_{d|n} A001783(d).
%e 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.
%t Table[Sum[Times @@ Select[Range@ d, CoprimeQ[#, d] &], {d, Divisors@ n}], {n, 27}] (* _Michael De Vlieger_, Jan 01 2017 *)
%o (Magma) [&+[&*[h: h in [1..d] | GCD(h,d) eq 1]: d in Divisors(n)]: n in [1..100]]
%o (PARI) a(n) = sumdiv(n, d, prod(k=1, d, if (gcd(k,d)==1, k, 1))); \\ _Michel Marcus_, Jan 02 2017
%Y Cf. A001783, A001105, A183300, A280259, A280260.
%K nonn
%O 1,2
%A _Jaroslav Krizek_, Jan 01 2017