OFFSET
1,3
COMMENTS
Exponent of highest power of 2 dividing Euler phi of primorials.
Conjecture: a(n) ~ 2n. - Charles R Greathouse IV, Jun 02 2015
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
EXAMPLE
For n=6, 6th primorial is 30030, phi(30030) = 5760 = 2^7 * 3^2 * 5, so a(6) = 7.
MAPLE
a:= proc(n) option remember; `if`(n<2, 0,
a(n-1)+padic[ordp](ithprime(n)-1, 2))
end:
seq(a(n), n=1..80); # Alois P. Heinz, Jan 01 2023
MATHEMATICA
Table[IntegerExponent[EulerPhi[Product[Prime[i], {i, n}]], 2], {n, 110}] (* Jamie Morken, Oct 13 2023 *)
PROG
(PARI) a(n) = sum(k=1, n, valuation(prime(k)-1, 2)); \\ Michel Marcus, May 30 2015
(PARI) a(n) = valuation(eulerphi(prod(k=1, n, prime(k))), 2); \\ Michel Marcus, May 30 2015
(PARI) first(n)=my(p=primes(n), s); vector(#p, i, s+=valuation(p[i]-1, 2)) \\ Charles R Greathouse IV, Jun 02 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Nov 02 2000
STATUS
approved