A076358 a(n) = numerator(n!/phi(n!)).

1, 2, 3, 3, 15, 15, 35, 35, 35, 35, 77, 77, 1001, 1001, 1001, 1001, 17017, 17017, 323323, 323323, 323323, 323323, 676039, 676039, 676039, 676039, 676039, 676039, 2800733, 2800733, 86822723, 86822723, 86822723, 86822723, 86822723, 86822723

Offset: 1

Author

Labos Elemer, Oct 08 2002

Keywords

• easy
• nonn
• frac

Comments

Denominator of Product_{p<=n, p prime} (1 - 1/p). - Franz Vrabec, Jan 28 2014

Links

• David A. Corneth, Table of n, a(n) for n = 1..2926

Crossrefs

Cf. A000005, A000142, A048855, A076359.

Programs

Mathematica

Numerator[#/EulerPhi[#]]&/@(Range[40]!) (* Harvey P. Dale, Apr 16 2016 *)

PARI

a(n) = denominator(prod(p=1, n, if (isprime(p),(1-1/p), 1))); \\ Michel Marcus, Jan 28 2014

PARI

first(n) = {my(res = vector(n), q = 2); res[1] = 1; res[2] = 1/2; forprime(p = 3, n, for(k = q + 1, p - 1, res[k] = res[k-1] ); res[p] = res[p-1]*(1-1/p); q = p; ); for(k = precprime(n)+1, n, res[k] = res[k-1] ); vector(n, i, denominator(res[i])) } \\ David A. Corneth, May 22 2020

Formula

a(n) = numerator(A000142(n)/A048855(n)).