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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 (list; graph; refs; listen; history; text; internal format)
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 n-th 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

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Last modified March 28 02:00 EDT 2017. Contains 284182 sequences.