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A307088 The position function the fractalization of which yields A307081. 2
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, 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, 18, 50, 21, 30, 2, 60, 2, 31, 38, 56, 20, 51, 2, 47, 25, 52, 2, 71 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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.

LINKS

Table of n, a(n) for n=1..72.

FORMULA

a(n)=1 iff n=1.

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

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

EXAMPLE

In A307081 in triangular form,

- row 8 is:  1  7  5  3  2  4  6  8

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

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

PROG

(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}

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, ", ")))}

CROSSREFS

Cf. A194959 (introducing fractalization).

Cf. A307081 (fractalization of this sequence).

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

Cf. A095112.

Sequence in context: A316437 A137502 A318885 * A143112 A286472 A279690

Adjacent sequences:  A307085 A307086 A307087 * A307089 A307090 A307091

KEYWORD

nonn

AUTHOR

Luc Rousseau, Mar 23 2019

STATUS

approved

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Last modified March 30 08:46 EDT 2020. Contains 333123 sequences. (Running on oeis4.)