A286250 Filter-sequence: a(n) = A278223(A064216(n)) = A046523((2*A064216(n))-1).

1, 2, 2, 4, 2, 2, 6, 2, 4, 6, 2, 2, 2, 6, 12, 6, 8, 2, 2, 2, 2, 16, 2, 6, 4, 6, 6, 2, 2, 30, 12, 6, 6, 4, 12, 6, 6, 6, 6, 6, 2, 2, 6, 6, 30, 2, 6, 2, 6, 6, 2, 6, 2, 6, 6, 6, 6, 2, 6, 6, 2, 12, 2, 36, 2, 6, 4, 2, 12, 30, 12, 12, 2, 12, 2, 24, 2, 2, 6, 6, 24, 2, 2, 12, 2, 24, 12, 2, 2, 30, 30, 6, 6, 2, 2, 4, 6, 2, 30, 6, 32, 2, 6, 2, 6, 2, 6, 12, 4, 2, 30, 2, 2

Offset: 1

Author

Antti Karttunen, May 07 2017

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A046523, A064216, A245448, A278223, A286243.

Programs

PARI

A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ This function from Charles R Greathouse IV, Aug 17 2011
A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
A064216(n) = A064989((2*n)-1);
A286250(n) = A046523(-1+(2*A064216(n)));
for(n=1, 10000, write("b286250.txt", n, " ", A286250(n)));

Python

from sympy import factorint, prevprime
from operator import mul
def P(n):
    f = factorint(n)
    return sorted([f[i] for i in f])
def a046523(n):
    x=1
    while True:
        if P(n) == P(x): return x
        else: x+=1
def a064216(n):
    f=factorint(2*n - 1)
    return 1 if n==1 else reduce(mul, [prevprime(i)**f[i] for i in f])
def a(n): return a046523((2*a064216(n)) - 1) # Indranil Ghosh, May 13 2017

Scheme

(define (A286250 n) (A046523 (+ -1 (* 2 (A064216 n)))))

Formula

a(n) = A046523(A245448(n)) = A278223(A064216(n)) = A046523((2*A064216(n))-1).