

A179312


Largest semiprime dividing n, or 0 if no semiprime divides n.


3



0, 0, 0, 4, 0, 6, 0, 4, 9, 10, 0, 6, 0, 14, 15, 4, 0, 9, 0, 10, 21, 22, 0, 6, 25, 26, 9, 14, 0, 15, 0, 4, 33, 34, 35, 9, 0, 38, 39, 10, 0, 21, 0, 22, 15, 46, 0, 6, 49, 25, 51, 26, 0, 9, 55, 14, 57, 58, 0, 15, 0, 62, 21, 4, 65, 33, 0, 34, 69, 35, 0, 9, 0, 74
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OFFSET

1,4


COMMENTS

a(p in primes A000040) = 0; a(k in semiprimes A001358) = k. This is to semiprimes A001358 as A006530 is to primes A000040.


LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..10000


FORMULA

a(n) = MAX(0, k in A001358 such that k  n).


EXAMPLE

The smallest semiprime is 4, so a(n<4) = 0.
a(4) = 4, since 4 = 2^2 is semiprime, and 4  4 (i.e. 4/4 = 1).
a(5) = 0 because 5 is prime, only 1 and 5 evenly divide 5, no prime (with 1 prime factor) is a semiprimes (with two prime factors, not necessarily distinct).
a(6) = 6, since 6 = 2*3 is semiprime, and 6  ^ (i.e. 6/6 = 1).
a(8) = 4, since 4 = 2^2 is semiprime, and 4  8 (i.e. 8/4 = 2).


MAPLE

a:= proc(n) local l;
if n<4 or isprime(n) then 0
else l:= sort(ifactors(n)[2], (x, y)> x[1]>y[1]);
l[1][1] *l[`if`(l[1][2]>=2, 1, 2)][1]
fi
end:
seq(a(n), n=1..80); # Alois P. Heinz, Jun 23 2012


MATHEMATICA

semiPrimeQ[n_] := Plus @@ Last /@ FactorInteger@ n == 2; f[n_] := Max@ Select[ Divisors@ n, semiPrimeQ] /. {\[Infinity] > 0}; Array[f, 55]


CROSSREFS

Cf. A001358, A006530, A034699, A052126, A052369, A061395
Cf. A088739 (smallest semiprime divisor of nth composite number)
Sequence in context: A016681 A210625 A210615 * A076290 A198224 A178105
Adjacent sequences: A179309 A179310 A179311 * A179313 A179314 A179315


KEYWORD

nonn,easy


AUTHOR

Jonathan Vos Post, Jan 11 2011


STATUS

approved



