A353757 - OEIS

%I #12 May 12 2022 16:12:57

%S 0,3,-2,28,-8,4,-26,44,108,12,-62,52,-102,-14,-32,862,-184,504,-282,

%T 96,-104,-22,-402,80,690,-12,-96,60,-596,48,-854,704,-248,-64,-328,

%U 3912,-810,-210,-408,240,-1360,-56,-1582,100,240,-322,-1946,1708,174,3300,-736,786,-2300,48,-744,72,-1128,-356,-2978,384

%N a(n) = A353750(n) - A353749(n).

%C It is conjectured that there are no other zeros after a(1) = 0.

%H Antti Karttunen, <a href="/A353757/b353757.txt">Table of n, a(n) for n = 1..10000</a>

%H Antti Karttunen, <a href="/A353757/a353757.txt">Data supplement: n, a(n) computed for n = 1..65537</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>

%F a(n) = A353750(n) - A353749(n) = A353749(A000203(n)) - A353749(n).

%o (PARI)

%o A064989(n) = { my(f=factor(n>>valuation(n,2))); for(i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f); };

%o A353749(n) = (eulerphi(n)*A064989(n));

%o A353757(n) = { my(s=sigma(n)); (A353749(s)-A353749(n)); };

%Y Cf. A000203, A064989, A353749, A353750, A353758 (positions of negative terms), A353759 (of terms >= 0), A353760.

%Y Cf. also A348736.

%K sign

%O 1,2

%A _Antti Karttunen_, May 10 2022