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

Offset: 0

Author

Antti Karttunen, Sep 26 2016

Keywords

• nonn
• base

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

Crossrefs

Left inverse of A277022.

Cf. A005940, A276085.

Cf. also A277017.

Programs

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

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)))))

Formula

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

Other identities. For all n >= 0:

a(A277022(n)) = n.