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 A196442 a(1) = a(2) = 1; for n >= 2, a(n) is the product of number k <= n such that GCQ_A(n, k) >= 2 (see definition in comments). 8
 1, 1, 3, 4, 60, 30, 2520, 6720, 45360, 604800, 19958400, 3991680, 3113510400, 14529715200, 163459296000, 3487131648000, 177843714048000, 266765571072000, 60822550204416000, 67580611338240000, 6386367771463680000, 187333454629601280000, 12926008369442488320000, 5170403347776995328000, 7755605021665492992000000, 67215243521100939264000000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Definition of GCQ_A: The greatest common non-divisor of type A (GCQ_A) of two positive integers a and b (a<=b) is the largest positive non-divisor q of numbers a and b such that 1<=q<=a common to a and b; GCQ_A(a, b) = 0 if no such c exists. GCQ_A(1, b) = GCQ_A(2, b) = 0 for b >=1. GCQ_A(a, b) = 0 or >= 2. a(n) is also the sum of number k <= n such that LCQ_A(n, k) >= 2. Definition of LCQ_A: The least common non-divisor of type A (LCQ_A) of two positive integers a and b (a<=b) is the least positive non-divisor q of numbers a and b such that 1<=q<=a common to a and b; LCQ_A(a, b) = 0 if no such c exists. LCQ_A(1, b) = LCQ_A(2, b) = 0 for b >=1. LCQ_A(a, b) = 0 or >= 2. LINKS FORMULA a(n) = A000142(n) / A196441(n). EXAMPLE For n = 6, a(6) = 30 because there are 2 cases k (k = 5, 6) with GCQ_A(6, k) >= 2: GCQ_A(6, 5) = 4, GCQ_A(6, 6) = 5 and the product of these numbers k is 30. Also there are 2 same cases k with LCQ_A(6, k) >= 2: LCQ_A(6, 5) = 4, LCQ_A(6, 6) = 4. PROG (PARI) GCQ_A(a, b) = { forstep(m=min(a, b)-1, 2, -1, if(a%m && b%m, return(m))); 0; }; \\ From PARI-program in A196438. A196442(n) = prod(k=1, n, if(2<=GCQ_A(n, k), k, 1)); \\ Antti Karttunen, Jun 13 2018 CROSSREFS Cf. A196437, A196438, A196439, A196440, A196441, A196442, A196443, A196444. Sequence in context: A331725 A067093 A041105 * A278035 A079076 A274699 Adjacent sequences:  A196439 A196440 A196441 * A196443 A196444 A196445 KEYWORD nonn AUTHOR Jaroslav Krizek, Nov 26 2011 EXTENSIONS More terms from Antti Karttunen, Jun 13 2018 STATUS approved

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Last modified September 21 10:03 EDT 2020. Contains 337268 sequences. (Running on oeis4.)