A307088 - OEIS

%I #12 May 23 2019 14:37:59

%S 1,2,2,4,2,6,2,8,5,7,2,12,2,9,9,15,2,17,2,19,10,13,2,24,9,15,13,23,2,

%T 28,2,29,13,19,13,35,2,21,15,37,2,37,2,32,29,24,2,48,14,34,19,37,2,48,

%U 18,50,21,30,2,60,2,31,38,56,20,51,2,47,25,52,2,71

%N The position function the fractalization of which yields A307081.

%C For a definition of the fractalization process, see comments in A194959. The sequence A307081, triangular array where row n is the list of the numbers from 1 to n sorted in ascending order of f(n) = A095112(n)/n, is clearly the result of a fractalization. Let {a(n)} (this sequence) be its position function.

%F a(n)=1 iff n=1.

%F a(n)=2 iff n is a prime number.

%F a(n)=n iff n is in A307187.

%e In A307081 in triangular form,

%e - row 8 is:  1  7  5  3  2  4  6  8

%e - row 9 is:  1  7  5  3  9  2  4  6  8

%e Row 9 is row 8 in which 9 has been inserted in position 5, so a(9) = 5.

%o (PARI) f(n)={my(s=0,T); T=factorint(n); for(i=1, #T[,1], for(j=1, T[i,2], s+=1/T[i,1]^j)); s}

%o prog(n)={my(V,v,j); V=List(); for(k=1, n, v=f(k)+0.; j=setsearch(V,v,1); if(j==0, print("err"); return, listinsert(V,v,j); print1(j,", ")))}

%Y Cf. A194959 (introducing fractalization).

%Y Cf. A307081 (fractalization of this sequence).

%Y Cf. A307187 (positions of the records of f).

%Y Cf. A095112.

%K nonn

%O 1,2

%A _Luc Rousseau_, Mar 23 2019