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A347115 Möbius transform of A341515.

%I A347115 #12 Oct 15 2021 21:32:44
%S A347115 1,4,1,10,2,5,4,30,2,118,6,12,10,236,2,90,12,64,16,240,4,594,18,36,6,
%T A347115 830,4,480,22,-116,28,270,6,1428,8,132,30,1784,10,720,36,1076,40,1200,
%U A347115 4,2622,42,108,20,144,12,1680,46,458,12,1440,16,4178,52,-228,58,4772,8,810,20,1242,60,2880,18,2752,66,396
%N A347115 Möbius transform of A341515.
%H A347115 Antti Karttunen, <a href="/A347115/b347115.txt">Table of n, a(n) for n = 1..10000</a>
%H A347115 <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>
%H A347115 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A347115 a(n) = A008683(n/d) * A341515(d).
%o A347115 (PARI)
%o A347115 A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
%o A347115 A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
%o A347115 A156552(n) = { my(f = factor(n), p, p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res };
%o A347115 A329603(n) = A005940(2+(3*A156552(n)));
%o A347115 A341515(n) = if(n%2, A064989(n), A329603(n));
%o A347115 A347115(n) = sumdiv(n,d,moebius(n/d)*A341515(d));
%Y A347115 Cf. A008683, A064989, A329603, A341515.
%Y A347115 Cf. A285702 (odd bisection), A347116 (even bisection).
%Y A347115 Cf. also A332463, A347117, A347118, A348045.
%K A347115 sign
%O A347115 1,2
%A A347115 _Antti Karttunen_, Aug 20 2021