A340141 Numerators of the sequence whose Dirichlet convolution with itself yields sequence A160595(x) = phi(x)/gcd(phi(x), x-1).

1, 1, 1, 7, 1, 3, 1, 25, 11, 7, 1, 19, 1, 11, 7, 363, 1, 31, 1, 43, 5, 19, 1, 63, 19, 23, 61, 3, 1, 15, 1, 1335, 9, 31, 23, 189, 1, 35, 23, 139, 1, 29, 1, 115, 23, 43, 1, 867, 27, 127, 31, 11, 1, 163, 39, 279, 17, 55, 1, 73, 1, 59, 123, 9923, 5, -15, 1, 187, 21, -9, 1, 615, 1, 71, 127, 19, 29, 47, 1, 1875, 1363, 79, 1, 203, 31

Offset: 1

Author

Antti Karttunen, Dec 29 2020

Keywords

• sign
• frac

Links

• Antti Karttunen, Table of n, a(n) for n = 1..8191
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Crossrefs

Cf. A046644 (denominators).

Cf. A160595.

Cf. also A340142, A340143.

Programs

PARI

up_to = 65537;
A160595(n) = { my(x=eulerphi(n)); x/gcd(x,n-1); };
DirSqrt(v) = {my(n=#v, u=vector(n)); u[1]=1; for(n=2, n, u[n]=(v[n]/v[1] - sumdiv(n, d, if(d>1&&dA160595(n)));
A340141(n) = numerator(v340141rat[n]);