

A057773


Sum_{i=1..n} nu_2 ( prime(i)  1), where prime(i) is the ith prime and nu_2(m) = exponent of highest power of 2 dividing m.


2



0, 1, 3, 4, 5, 7, 11, 12, 13, 15, 16, 18, 21, 22, 23, 25, 26, 28, 29, 30, 33, 34, 35, 38, 43, 45, 46, 47, 49, 53, 54, 55, 58, 59, 61, 62, 64, 65, 66, 68, 69, 71, 72, 78, 80, 81, 82, 83, 84, 86, 89, 90, 94, 95, 103, 104, 106, 107, 109, 112, 113, 115, 116, 117, 120, 122, 123
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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


FORMULA

a(n) = A007814(A000010(A002110(n))).


EXAMPLE

n=6, 6th primorial is 30030, Phi(30030)=5760=128.9.5, so a(6)=7, exponent of 128.


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

Cf. A007814, A000010, A002110.
Sequence in context: A022440 A088130 A046840 * A020486 A091428 A047499
Adjacent sequences: A057770 A057771 A057772 * A057774 A057775 A057776


KEYWORD

nonn


AUTHOR

Labos Elemer, Nov 02 2000


STATUS

approved



