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A286163 Compound filter: a(n) = T(A046523(n), A278222(n)), where T(n,k) is sequence A000027 used as a pairing function. 15
2, 5, 12, 14, 23, 42, 38, 44, 40, 61, 80, 117, 80, 84, 216, 152, 23, 148, 80, 148, 601, 142, 302, 375, 109, 142, 911, 183, 302, 1020, 530, 560, 61, 61, 142, 856, 467, 142, 412, 430, 467, 1741, 1832, 265, 2497, 412, 1178, 1323, 109, 265, 826, 265, 1832, 1735, 2932, 489, 412, 412, 2630, 2835, 1178, 672, 2787, 2144, 61, 625, 80, 148, 601, 850, 302, 2998, 467, 601 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

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

MathWorld, Pairing Function

FORMULA

a(n) = (1/2)*(2 + ((A046523(n)+A278222(n))^2) - A046523(n) - 3*A278222(n)).

PROG

(PARI)

A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t }; \\ Modified from code of M. F. Hasler

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

A278222(n) = A046523(A005940(1+n));

A286163(n) = (2 + ((A046523(n)+A278222(n))^2) - A046523(n) - 3*A278222(n))/2;

for(n=1, 10000, write("b286163.txt", n, " ", A286163(n)));

(Scheme) (define (A286163 n) (* (/ 1 2) (+ (expt (+ (A046523 n) (A278222 n)) 2) (- (A046523 n)) (- (* 3 (A278222 n))) 2)))

(Python)

from sympy import prime, factorint

import math

def T(n, m): return ((n + m)**2 - n - 3*m + 2)/2

def A(n): return n - 2**int(math.floor(math.log(n, 2)))

def b(n): return n + 1 if n<2 else prime(1 + (len(bin(n)[2:]) - bin(n)[2:].count("1"))) * b(A(n))

def a005940(n): return b(n - 1)

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 a278222(n): return a046523(a005940(n + 1))

def a(n): return T(a046523(n), a278222(n)) # Indranil Ghosh, May 05 2017

CROSSREFS

Cf. A000027, A046523, A278222, A286160, A286161, A286162, A286164.

Sequence in context: A114217 A286255 A286160 * A286240 A215974 A192524

Adjacent sequences:  A286160 A286161 A286162 * A286164 A286165 A286166

KEYWORD

nonn

AUTHOR

Antti Karttunen, May 04 2017

STATUS

approved

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Last modified January 21 04:53 EST 2020. Contains 331104 sequences. (Running on oeis4.)