A240502 Product of primes appearing in the factorization of n! with even exponents.

1, 1, 1, 1, 1, 1, 6, 6, 3, 3, 30, 30, 10, 10, 35, 21, 21, 21, 42, 42, 210, 10, 55, 55, 330, 330, 2145, 715, 5005, 5005, 6006, 6006, 3003, 91, 3094, 2210, 2210, 2210, 20995, 4845, 1938, 1938, 2261, 2261, 24871, 124355, 5720330, 5720330, 17160990, 17160990, 8580495

Offset

0,7

Comments

All terms are squarefree (A005117). - Michel Marcus, Feb 15 2016

Links

David A. Corneth, Table of n, a(n) for n = 0..7585

Formula

a(n) = rad(n!)/core(n!) = A336643(n!). - Benoit Cloitre, Mar 12 2022

Example

In the prime power factorization 2^7*3^4*5*7 of 9! only the exponent of 3 is even. Thus a(9)=3.

Mathematica

Table[Times@@Select[FactorInteger[n!], EvenQ[#[[2]]]&][[;; , 1]], {n, 0, 50}] (* Harvey P. Dale, Feb 24 2023 *)

Prog

(PARI) a(n) = {my(f = factor(n!)); for (k=1, #f~, f[k, 2] = 1 - (f[k, 2] % 2); ); factorback(f); } \\ Michel Marcus, Feb 15 2016
(PARI) a(n) = {my(res=1); forprime(p=2, n\2, e=val(n, p); if(e%2==0, res*=p)); res}
val(n, p) = my(r=0); while(n, r+=n\=p); r \\ David A. Corneth, Feb 24 2023

Crossrefs

Cf. A000142, A005117, A055204.

Sequence in context: A146761 A010498 A339083 * A112112 A193085 A338004

Adjacent sequences: A240499 A240500 A240501 * A240503 A240504 A240505

Keyword

nonn

Author

Vladimir Shevelev, Apr 06 2014

Extensions

More terms from Michel Marcus, Feb 15 2016

Status

approved