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 A320672 a(n) is the smallest divisor of (n+2)*(n+3) not yet in the sequence. 0
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 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, ... LINKS EXAMPLE 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. 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 *) PROG (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 CROSSREFS Cf. A002378, A111273, A246368. Sequence in context: A035506 A246368 A316963 * A006016 A227413 A217122 Adjacent sequences:  A320669 A320670 A320671 * A320673 A320674 A320675 KEYWORD nonn AUTHOR Enrique Navarrete, Oct 19 2018 STATUS approved

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Last modified January 27 10:39 EST 2022. Contains 350607 sequences. (Running on oeis4.)