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%I #6 Nov 11 2019 15:41:10
%S 1,2,2,4,2,5,2,8,5,7,2,11,2,9,7,16,2,14,2,17,9,13,2,23,9,15,14,23,2,
%T 22,2,32,13,19,11,32,2,21,15,37,2,30,2,35,22,25,2,47,14,34,19,41,2,41,
%U 17,51,21,31,2,52,2,33,30,64,19,46,2,53,25,46,2,68,2
%N The position function the fractalization of which yields A328719.
%C For a definition of the fractalization process, see comments in A194959. The sequence A328719, triangular array where row n is the list of the numbers k from 1 to n sorted in ascending lexicographic order of their sequences of p-adic valuations, is clearly the result of a fractalization. Let {a(n)} (this sequence) be its position function.
%F a(1) = 1.
%F a(p) = 2 iff p is a prime number.
%F a(2^k) = 2^k.
%F a(3^k) = (3^k+1)/2 = A007051(k).
%F A328719(n, a(n)) = n. - _Rémy Sigrist_, Nov 11 2019
%e In A328719 in triangular form, rows 19 and 20 are:
%e 1, 19, 17, 13, 11, 7, 5, 3, 15, 9, 2, 14, 10, 6, 18, 4, 12, 8, 16;
%e 1, 19, 17, 13, 11, 7, 5, 3, 15, 9, 2, 14, 10, 6, 18, 4, 20, 12, 8, 16.
%e Row 20 is row 19 in which 20 has been inserted in position 17, so a(20) = 17.
%o (PARI) L=List();n=1;while(n<=100,i=1;while(i<n&&factor(L[i]/n)[1,2]<0,i++);listinsert(L,n,i);print1(i,", ");n++)
%Y Cf. A007051, A194959, A328719.
%K nonn
%O 1,2
%A _Luc Rousseau_, Oct 26 2019
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