A280246 a(n) = Product_{d|n} psi(d), where psi(m) is the sum of totatives of m (A023896).

1, 1, 3, 4, 10, 18, 21, 64, 81, 200, 55, 1728, 78, 882, 1800, 4096, 136, 26244, 171, 64000, 7938, 6050, 253, 2654208, 2500, 12168, 19683, 592704, 406, 25920000, 465, 1048576, 54450, 36992, 88200, 544195584, 666, 58482, 109512, 327680000, 820, 504094752, 903

Offset: 1

Author

Jaroslav Krizek, Dec 30 2016

Keywords

• nonn

Comments

a(n) = n only for n = 1, 3 and 4.

n divides a(n) for all n except 2.

Conjecture: a(n) is odd iff the sum of totatives of n (A023896) is odd.

Examples

			For n=6; sets of totatives of divisors of 6: {1}, {1}, {1, 2}, {1, 5}; a(6) = 1*1*(1+2)*(1+5) = 18.
		

Crossrefs

Cf. A023896, A057661, A280247, A280248.

Programs

Magma

[&*[&+[h: h in [1..d] | GCD(h,d) eq 1]: d in Divisors(n)]: n in [1..100]]

Mathematica

Table[Product[Total@ Select[Range@ d, CoprimeQ[d, #] &], {d, Divisors@ n}], {n, 43}] (* Michael De Vlieger, Dec 30 2016 *)

Formula

a(n) = Product_{d|n} A023896(d).