A285323 -id:A285323 - cp's OEIS frontend

A285110 a(n) = A001222(A285323(n)).

0, 2, 2, 1, 2, 2, 1, 1, 2, 2, 1, 1, 1, 2, 1, 1, 2, 2, 2, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 2, 2, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 2, 2, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1

Offset: 0

Antti Karttunen, Apr 19 2017

nonn

The sequence is completely determined by the positions of two least significant 1-bits of n: After initial zero, if n is a power of two (only one 1-bit present) or if prime(1+A285099(n)) > prime(1+A007814(n))^2, a(n) = 2, otherwise a(n) = 1.

Antti Karttunen, Table of n, a(n) for n = 0..8192

Cf. A000040, A000290, A001222, A007814, A285099, A285323, A285324.

from operator import mul
from sympy import prime, primefactors
from functools import reduce
def a001222(n): return 0 if n<2 else a001222(n//min(primefactors(n))) + 1
def a019565(n): return reduce(mul, (prime(i+1) for i, v in enumerate(bin(n)[:1:-1]) if v == '1')) if n > 0 else 1 # This function from Chai Wah Wu
def a007947(n): return 1 if n<2 else reduce(mul, primefactors(n))
def a065642(n):
    if n==1: return 1
    r=a007947(n)
    n += r
    while a007947(n)!=r:
        n+=r
    return n
def a285323(n): return a065642(a065642(a019565(n)))//a019565(n)
def a(n): return a001222(a285323(n))
print([a(n) for n in range(121)]) # Indranil Ghosh, Apr 20 2017

(define (A285110 n) (A001222 (A285323 n)))
(define (A285110 n) (cond ((zero? n) n) ((or (= 1 (A000120 n)) (> (A000040 (+ 1 (A285099 n))) (A000290 (A000040 (+ 1 (A007814 n)))))) 2) (else 1)))

a(n) = A001222(A285323(n)).

A285327 Row 3 of A285325: a(n) = A048675(A065642(A065642(A019565(n)))).

Original entry on oeis.org

0, 3, 6, 5, 12, 7, 10, 9, 24, 11, 18, 13, 20, 15, 18, 17, 48, 19, 22, 21, 36, 23, 26, 25, 40, 27, 34, 29, 36, 31, 34, 33, 96, 35, 38, 37, 68, 39, 42, 41, 72, 43, 50, 45, 52, 47, 50, 49, 80, 51, 54, 53, 68, 55, 58, 57, 72, 59, 66, 61, 68, 63, 66, 65, 192, 67, 70, 69, 132, 71, 74, 73, 136, 75, 82, 77, 84, 79, 82, 81, 144, 83, 86, 85, 100, 87, 90, 89

Offset: 0

Antti Karttunen, Apr 19 2017

nonn

Antti Karttunen, Table of n, a(n) for n = 0..8191

Row 3 of A285325 (after the initial zero).

Cf. A007947, A019565, A048675, A065642, A285323, A285324.

A019565(n) = {my(j,v); factorback(Mat(vector(if(n, #n=vecextract(binary(n), "-1..1")), j, [prime(j), n[j]])~))}; \\ This function from M. F. Hasler
A048675(n) = my(f = factor(n)); sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2; \\ Michel Marcus, Oct 10 2016
A007947(n) = factorback(factorint(n)[, 1]); \\ From Andrew Lelechenko, May 09 2014
A065642(n) = { my(r=A007947(n)); if(1==n,n,n = n+r; while(A007947(n) <> r, n = n+r); n); };
A285327(n) = A048675(A065642(A065642(A019565(n))));

(define (A285327 n) (A048675 (A065642 (A065642 (A019565 n)))))

a(n) = A048675(A065642(A065642(A019565(n)))).

cp's OEIS Frontend

A285110 a(n) = A001222(A285323(n)).

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