A210615 Least semiprime dividing n, or 0 if no semiprime divides n.

0, 0, 0, 4, 0, 6, 0, 4, 9, 10, 0, 4, 0, 14, 15, 4, 0, 6, 0, 4, 21, 22, 0, 4, 25, 26, 9, 4, 0, 6, 0, 4, 33, 34, 35, 4, 0, 38, 39, 4, 0, 6, 0, 4, 9, 46, 0, 4, 49, 10, 51, 4, 0, 6, 55, 4, 57, 58, 0, 4, 0, 62, 9, 4, 65, 6, 0, 4, 69, 10, 0, 4, 0, 74, 15, 4, 77, 6

Offset

1,4

Comments

Roughly analogous to Least Prime Factor A020639 but with semiprimes rather than primes.

Links

T. D. Noe, Table of n, a(n) for n = 1..1000

Formula

a(n) = min {k such that k|n and k in A001358} else 0 if there exists no such k.

a(p) = 0 iff p in A008578. - Alois P. Heinz, Mar 28 2012

Example

a(24) = 4 because 24 is divisible by the semiprimes {4,6} of which 4 is the smallest.

Mathematica

Table[If[PrimeQ[n] || n < 2, 0, f = FactorInteger[n]; If[f[[1, 2]] > 1, f[[1, 1]]^2, f[[1, 1]]*f[[2, 1]]]], {n, 100}] (* T. D. Noe, Mar 24 2012 *)
Flatten[Table[Select[Divisors[n], PrimeOmega[#]==2&, 1], {n, 80}]/.{}->{0}] (* Harvey P. Dale, Dec 07 2012 *)

Crossrefs

Cf. A001358, A008578, A020639, A088739 (this sequence without the zeros).

Sequence in context: A125961 A016681 A210625 * A179312 A076290 A198224

Adjacent sequences: A210612 A210613 A210614 * A210616 A210617 A210618

Keyword

nonn,easy

Author

Jonathan Vos Post, Mar 23 2012

Status

approved