A320672 a(n) is the smallest divisor of (n+2)*(n+3) not yet in the sequence.

1, 2, 4, 3, 6, 7, 8, 5, 10, 11, 12, 13, 14, 15, 16, 9, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 17, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 33, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 44, 56, 57, 58, 59, 60, 61, 62, 63, 64, 55, 66, 67, 68, 69, 70

Offset: 0

Author

Enrique Navarrete, Oct 19 2018

Keywords

• nonn

Comments

a(n) is the smallest divisor of A002378(n+2) not yet in the sequence.

The numbers that are smaller than the preceding terms are: 3, 5, 9, 17, 33, 44, 55, 65, 90, 99, 143, 208, ...

Examples

			For n = 0, a(0) = 1 since 1 is the smallest divisor of 6 not yet in the sequence.
For n = 3, a(3) = 3 since 3 is the smallest divisor of 30 not yet in the sequence.
		

Crossrefs

Cf. A002378, A111273, A246368.

Programs

Mathematica

s = {}; Do[d = Divisors[(n + 2)(n + 3)]; Do[d1 = d[[k]]; If[FreeQ[s, d1], AppendTo[s, d1]; Break[]], {k, Length[d]}], {n, 0, 100}]; s (* Amiram Eldar, Nov 14 2018 *)

PARI

toadd(n, v) = {fordiv(n, d, if (!vecsearch(v, d), return(d)); ); }
lista(nn) = {v = []; for (n = 0, nn, newt = toadd((n+2)*(n+3), v); print1(newt, ", "); v = vecsort(concat(v, newt)); ); } \\ Michel Marcus, Nov 20 2018