A277892 a(n) = A001222(A048675(n)).

0, 1, 1, 2, 1, 3, 1, 2, 1, 4, 2, 5, 2, 2, 2, 6, 1, 7, 2, 2, 1, 8, 1, 3, 2, 2, 2, 9, 1, 10, 1, 3, 2, 3, 2, 11, 2, 2, 1, 12, 1, 13, 3, 3, 1, 14, 2, 4, 2, 3, 2, 15, 1, 3, 1, 3, 4, 16, 3, 17, 3, 3, 2, 4, 1, 18, 3, 3, 1, 19, 1, 20, 2, 2, 3, 4, 2, 21, 3, 3, 2, 22, 3, 3, 2, 2, 1, 23, 2, 4, 3, 5, 3, 4, 1, 24, 1, 3, 2, 25, 1, 26, 2, 2

Offset

2,4

Comments

For n >= 3, a(n) = index of the row where n is located in array A277898.

Links

Antti Karttunen (terms 2..3465) and Hans Havermann, Table of n, a(n) for n = 2..10000

Formula

a(A019565(n)) = a(A260443(n)) = A001222(n).

For all n >= 2, a(A065091(n)) = n.

Mathematica

A048675[n_] := If[n == 1, 0, Total[#[[2]]*2^(PrimePi[#[[1]]] - 1)& /@ FactorInteger[n]]];
a[n_] := PrimeOmega[A048675[n]];
Table[a[n], {n, 2, 105}] (* Jean-François Alcover, Jan 11 2022 *)

Prog

(Scheme) (define (A277892 n) (if (= 1 n) 0 (A001222 (A048675 n))))
(PARI)
A048675(n) = my(f = factor(n)); sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2;
A277892(n) = if(1==n, 0, bigomega(A048675(n)));
for(n=1, 3465, write("b277892.txt", n, " ", A277892(n)));
(Python)
from sympy import factorint, primepi, primefactors
def a001222(n): return 0 if n==1 else a001222(n//primefactors(n)[0]) + 1
def a048675(n):
    if n==1: return 0
    f=factorint(n)
    return sum(f[i]*2**(primepi(i) - 1) for i in f)
def a(n): return a001222(a048675(n))
print([a(n) for n in range(2, 101)]) # Indranil Ghosh, Jun 19 2017

Crossrefs

Left inverse of A065091.

Cf. A001222, A048675.

Cf. A277319 (positions of ones).

Cf. A000040 (positions of records), A277900.

Cf. A277895 (ordinal transform from a(3) onward).

Cf. A277893, A277894, A277898.

Sequence in context: A325565 A286552 A324826 * A214743 A331179 A026100

Adjacent sequences: A277889 A277890 A277891 * A277893 A277894 A277895

Keyword

nonn

Author

Antti Karttunen, Nov 08 2016

Status

approved