A277021 - OEIS

A277021

Left inverse of A277022.

0, 1, 2, 2, 6, 3, 4, 3, 30, 7, 8, 4, 12, 5, 6, 4, 210, 31, 32, 8, 36, 9, 10, 5, 60, 13, 14, 6, 18, 7, 8, 5, 2310, 211, 212, 32, 216, 33, 34, 9, 240, 37, 38, 10, 42, 11, 12, 6, 420, 61, 62, 14, 66, 15, 16, 7, 90, 19, 20, 8, 24, 9, 10, 6, 30030, 2311, 2312, 212, 2316, 213, 214, 33, 2340, 217, 218, 34, 222, 35, 36, 10, 2520, 241, 242

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

LINKS

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

Index entries for sequences related to binary expansion of n

Index entries for sequences related to primorial base

FORMULA

a(n) = A276085(A005940(1+n)).

Other identities. For all n >= 0:

a(A277022(n)) = n.

PROG

(Scheme)

(define (A277021 n) (let loop ((s 0) (n n) (r 0) (i 1) (pr 1)) (cond ((zero? n) (+ s (* r pr))) ((even? n) (loop (+ s (* r pr)) (/ n 2) 0 (+ 1 i) (* (A000040 i) pr))) (else (loop s (/ (- n 1) 2) (+ 1 r) i pr)))))

(Python)

from sympy import primorial, primepi, prime, factorint, floor, log

def a002110(n): return 1 if n<1 else primorial(n)

def a276085(n):

f=factorint(n)

return sum([f[i]*a002110(primepi(i) - 1) for i in f])

def A(n): return n - 2**int(floor(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 a(n): return a276085(b(n - 1))

print([a(n) for n in range(1, 101)]) # Indranil Ghosh, Jun 22 2017

CROSSREFS

Left inverse of A277022.