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A286251 Compound filter: a(n) = P(A001511(1+n), A046523(n)), where P(n,k) is sequence A000027 used as a pairing function. 7
3, 2, 9, 7, 5, 16, 14, 29, 12, 16, 9, 67, 5, 16, 50, 121, 5, 67, 9, 67, 23, 16, 14, 277, 12, 16, 48, 67, 5, 436, 27, 497, 23, 16, 31, 631, 5, 16, 40, 277, 5, 436, 9, 67, 80, 16, 20, 1129, 12, 67, 31, 67, 5, 277, 40, 277, 23, 16, 9, 1771, 5, 16, 160, 2017, 23, 436, 9, 67, 23, 436, 14, 2557, 5, 16, 94, 67, 23, 436, 20, 1129, 138, 16, 9, 1771, 23, 16, 40, 277, 5 (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 + ((A001511(1+n)+A046523(n))^2) - A001511(1+n) - 3*A046523(n)).

PROG

(PARI)

A001511(n) = (1+valuation(n, 2));

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

A286251(n) = (2 + ((A001511(1+n)+A046523(n))^2) - A001511(1+n) - 3*A046523(n))/2;

for(n=1, 10000, write("b286251.txt", n, " ", A286251(n)));

(Scheme) (define (A286251 n) (* (/ 1 2) (+ (expt (+ (A001511 (+ 1 n)) (A046523 n)) 2) (- (A001511 (+ 1 n))) (- (* 3 (A046523 n))) 2)))

(Python)

from sympy import factorint

def a001511(n): return 2 + bin(n - 1)[2:].count("1") - bin(n)[2:].count("1")

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

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 a(n): return T(a001511(n + 1), a046523(n)) # Indranil Ghosh, May 07 2017

CROSSREFS

Cf. A000027, A001511, A046523, A286161, A286252, A286253, A286254.

Sequence in context: A182950 A011323 A227630 * A072027 A061898 A021756

Adjacent sequences:  A286248 A286249 A286250 * A286252 A286253 A286254

KEYWORD

nonn

AUTHOR

Antti Karttunen, May 07 2017

STATUS

approved

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Last modified April 12 09:39 EDT 2021. Contains 342920 sequences. (Running on oeis4.)