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

Author

Jonathan Vos Post, Mar 23 2012

Keywords

• nonn
• easy

Comments

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

Examples

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

Links

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

Crossrefs

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

Programs

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 *)

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