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A336964 Irregular triangle in which first row is 1, n-th row (n > 1) lists distinct prime numbers in the prime tower factorization of n.

%I A336964 #14 Aug 13 2020 10:11:45
%S A336964 1,2,3,2,5,2,3,7,2,3,2,3,2,5,11,2,3,13,2,7,3,5,2,17,2,3,19,2,5,3,7,2,
%T A336964 11,23,2,3,2,5,2,13,3,2,7,29,2,3,5,31,2,5,3,11,2,17,5,7,2,3,37,2,19,3,
%U A336964 13,2,3,5,41,2,3,7,43,2,11,2,3,5,2,23,47,2,3
%N A336964 Irregular triangle in which first row is 1, n-th row (n > 1) lists distinct prime numbers in the prime tower factorization of n.
%C A336964 The prime tower factorization of a number is defined in A182318.
%C A336964 The n-th row includes the n-th row of A027748.
%H A336964 Rémy Sigrist, <a href="/A336964/b336964.txt">Table of n, a(n) for n = 1..10001</a> (rows for n = 1..4045)
%e A336964 Triangle begins:
%e A336964      1    [1]
%e A336964      2    [2]
%e A336964      3    [3]
%e A336964      4    [2]
%e A336964      5    [5]
%e A336964      6    [2, 3]
%e A336964      7    [7]
%e A336964      8    [2, 3]
%e A336964      9    [2, 3]
%e A336964     10    [2, 5]
%e A336964     11    [11]
%e A336964     12    [2, 3]
%e A336964     13    [13]
%e A336964     14    [2, 7]
%e A336964     15    [3, 5]
%o A336964 (PARI) row(n) = { my (f=factor(n), p=f[,1]~); for (k=1, #f~, if (f[k,2]>1, p=concat(p, row(f[k,2])));); if (#p==0, [1], Set(p)) }
%Y A336964 Cf. A027748, A115588 (row lengths), A182318, A336965.
%K A336964 nonn,tabf
%O A336964 1,2
%A A336964 _Rémy Sigrist_, Aug 09 2020