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%I #16 Feb 19 2020 22:36:21
%S 1,1,3,3,4,1,4,4,5,1,5,4,6,1,6,4,7,1,7,4,8,1,8,4,9,4,10,1,9,6,5,5,6,6,
%T 7,5,7,6,8,5,8,6,9,7,7,8,7,9,8,8,9,9,10,3,5,9,11,1,10,5,10,6,10,7,10,
%U 8,10,9,12,3,6,11,3,7,11,4,11,5,11,6,12,4
%N a(n+1) is the number of times a(n) is the product of one or more consecutive terms in this sequence so far with a(1) = 1.
%C This sequence is a multiplicative variant of A331614.
%C This sequence is unbounded.
%H Rémy Sigrist, <a href="/A332518/b332518.txt">Table of n, a(n) for n = 1..10000</a>
%H Rémy Sigrist, <a href="/A332518/a332518.txt">C program for A332518</a>
%e The first terms, alongside the corresponding products, are:
%e n a(n) Products
%e -- ---- --------
%e 1 1 a(1)
%e 2 1 a(1), a(1)*a(2), a(2)
%e 3 3 a(1)*a(2)*a(3), a(2)*a(3), a(3)
%e 4 3 a(1)*a(2)*a(3), a(2)*a(3), a(3), a(4)
%e 5 4 a(5)
%e 6 1 a(1), a(1)*a(2), a(2), a(6)
%e 7 4 a(5), a(5)*a(6), a(6)*a(7), a(7)
%e 8 4 a(5), a(5)*a(6), a(6)*a(7), a(7), a(8)
%e 9 5 a(9)
%e 10 1 a(1), a(1)*a(2), a(2), a(6), a(10)
%e 11 5 a(9), a(9)*a(10), a(10)*a(11), a(11)
%e 12 4 a(5), a(5)*a(6), a(6)*a(7), a(7), a(8), a(12)
%o (C) See Links section.
%Y Cf. A331614.
%K nonn
%O 1,3
%A _Rémy Sigrist_, Feb 15 2020
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