Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #13 May 08 2021 23:05:32
%S 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,
%T 18,7,8,5,2310,211,212,32,216,33,34,9,240,37,38,10,42,11,12,6,420,61,
%U 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
%N Left inverse of A277022.
%H Antti Karttunen, <a href="/A277021/b277021.txt">Table of n, a(n) for n = 0..8191</a>
%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%F a(n) = A276085(A005940(1+n)).
%F Other identities. For all n >= 0:
%F a(A277022(n)) = n.
%o (Scheme)
%o (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)))))
%o (Python)
%o from sympy import primorial, primepi, prime, factorint, floor, log
%o def a002110(n): return 1 if n<1 else primorial(n)
%o def a276085(n):
%o f=factorint(n)
%o return sum([f[i]*a002110(primepi(i) - 1) for i in f])
%o def A(n): return n - 2**int(floor(log(n, 2)))
%o def b(n): return n + 1 if n<2 else prime(1 + (len(bin(n)[2:]) - bin(n)[2:].count("1"))) * b(A(n))
%o def a(n): return a276085(b(n - 1))
%o print([a(n) for n in range(1, 101)]) # _Indranil Ghosh_, Jun 22 2017
%Y Left inverse of A277022.
%Y Cf. A005940, A276085.
%Y Cf. also A277017.
%K nonn,base
%O 0,3
%A _Antti Karttunen_, Sep 26 2016