A076358 - OEIS

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

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OFFSET

1,2

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

FORMULA

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

MATHEMATICA

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

PROG

(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

CROSSREFS

Cf. A000005, A000142, A048855, A076359.

Sequence in context: A109203 A362641 A039792 * A208798 A090522 A114728

Adjacent sequences: A076355 A076356 A076357 * A076359 A076360 A076361

KEYWORD

easy,nonn,frac

AUTHOR

Labos Elemer, Oct 08 2002

STATUS

approved