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Lexicographically earliest sequence of distinct positive terms that can be viewed as an irregular table where the n-th row has max(1, A001221(a(n))) terms and for n > 1, T(n, k) is a multiple of the k-th prime factor of a(n) (=A027748(a(n), k)).
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%I #13 Jan 09 2020 18:31:23

%S 1,2,3,4,5,6,9,12,8,15,10,18,20,14,25,16,21,22,30,24,7,35,26,27,28,32,

%T 11,34,33,40,36,39,42,45,49,38,13,48,44,56,46,55,50,17,51,66,52,60,54,

%U 57,63,65,58,69,70,72,75,77,62,19,78,64,81,68,88,74,84

%N Lexicographically earliest sequence of distinct positive terms that can be viewed as an irregular table where the n-th row has max(1, A001221(a(n))) terms and for n > 1, T(n, k) is a multiple of the k-th prime factor of a(n) (=A027748(a(n), k)).

%C This sequence is a permutation of the natural numbers:

%C - beyond the sixth row, every even number gives rise to another even number,

%C - so eventually every even number appears in the sequence,

%C - for any odd prime number p we will have infinitely many multiples of 2*p,

%C - giving rise to infinitely many multiples of p,

%C - and eventually every number will appear.

%H Rémy Sigrist, <a href="/A331016/b331016.txt">Table of n, a(n) for n = 1..10000</a>

%H Rémy Sigrist, <a href="/A331016/a331016.gp.txt">PARI program for A331016</a>

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

%e The first terms and rows are:

%e n a(n) row(n)

%e -- ---- ------------

%e 1 1 [1]

%e 2 2 [2]

%e 3 3 [3]

%e 4 4 [4]

%e 5 5 [5]

%e 6 6 [6, 9]

%e 7 9 [12]

%e 8 12 [8, 15]

%e 9 8 [10]

%e 10 15 [18, 20]

%e 11 10 [14, 25]

%o (PARI) See Links section.

%Y See A331010 for similar sequences.

%Y Cf. A001221, A027748.

%K nonn,look,tabf

%O 1,2

%A _Rémy Sigrist_, Jan 06 2020