

A270649


Greatest m such that 2^m divides p^2  q^2, where p = prime(n) and q is a prime < p.


2



0, 4, 3, 5, 5, 4, 6, 5, 6, 5, 6, 7, 6, 7, 7, 7, 7, 8, 7, 6, 6, 7, 6, 8, 7, 7, 7, 8, 7, 6, 8, 7, 8, 9, 8, 8, 7, 9, 9, 7, 8, 7, 8, 9, 8, 8, 7, 9, 8, 9, 9, 8, 9, 8, 9, 9, 10, 8, 8, 10, 9, 8, 8, 10, 9, 10, 8, 8, 10, 9, 9, 8, 10, 8, 9, 9, 8, 9, 10, 9, 9, 9, 10
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OFFSET

2,2


LINKS

Clark Kimberling, Table of n, a(n) for n = 2..10000


EXAMPLE

For n = 5, the numbers p^2  q^2 are 121  9 = 16*7, 121  25 = 32*3, 121  49 = 8*7, so that a(5) = 5.


MATHEMATICA

a[n_] := Max[Table[IntegerExponent[Prime[n]^2  Prime[m]^2, 2], {m, 1, n  1}]];
u = Table[a[n], {n, 2, 230}]


PROG

(PARI) a(n, p=prime(n))=if(p<5, return(0)); my(p2=p^2); forstep(k=logint(p29, 2), 1, 1, my(m=2^k, t); forstep(q=p2m, 9, m, if(issquare(q, &t) && isprime(t), return(k)))) \\ Charles R Greathouse IV, Apr 29 2016


CROSSREFS

Cf. A000040, A270651.
Sequence in context: A134186 A024688 A024477 * A049008 A280023 A170816
Adjacent sequences: A270646 A270647 A270648 * A270650 A270651 A270652


KEYWORD

nonn,easy


AUTHOR

Clark Kimberling, Apr 26 2016


STATUS

approved



