A280258 a(n) = Sum_{d|n} pxi(d), where pxi(m) is the product of totatives of m (A001783).

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

Offset

1,2

Comments

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, ...

Links

Robert G. Wilson v, Table of n, a(n) for n = 1..1000

Formula

a(n) = Sum_{d|n} A001783(d).

Example

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.

Mathematica

Table[Sum[Times @@ Select[Range@ d, CoprimeQ[#, d] &], {d, Divisors@ n}], {n, 27}] (* Michael De Vlieger, Jan 01 2017 *)

Prog

(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

Crossrefs

Cf. A001783, A001105, A183300, A280259, A280260.

Sequence in context: A256463 A279864 A324289 * A181730 A024774 A068543

Adjacent sequences: A280255 A280256 A280257 * A280259 A280260 A280261

Keyword

nonn

Author

Jaroslav Krizek, Jan 01 2017

Status

approved