A346239 - OEIS

%I #13 Aug 26 2021 10:56:19

%S 0,1,2,10,2,33,4,74,44,55,2,278,4,115,116,490,2,613,4,498,242,169,6,

%T 1942,92,265,742,1046,2,1591,6,3086,344,355,330,4986,4,487,542,3570,2,

%U 3347,4,1638,2326,737,6,12542,376,2121,716,2546,6,9869,388,7510,986,943,2,12894,6,1225,4872,18970,630,5353,4,3498,1492

%N Möbius transform of A341512, sigma(n)*A003961(n) - n*sigma(A003961(n)).

%H Antti Karttunen, <a href="/A346239/b346239.txt">Table of n, a(n) for n = 1..16384</a>

%H <a href="/index/Pri#gaps">Index entries for primes, gaps between</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) = Sum_{d|n} A008683(n/d) * A341512(d).

%F a(n) = A341512(n) - A346240(n).

%F a(n) = A347125(n) - A347124(n). - _Antti Karttunen_, Aug 25 2021

%o (PARI)

%o A003961(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); }; \\ From A003961

%o A341528(n) = (n*sigma(A003961(n)));

%o A341529(n) = (sigma(n)*A003961(n));

%o A341512(n) = (A341529(n)-A341528(n));

%o A346239(n) = sumdiv(n,d,moebius(n/d)*A341512(d));

%Y Cf. A000203, A003961, A008683, A341528, A341529, A341512, A346240, A347096, A347124, A347125.

%Y Cf. also the sequences A001359, A029710, A031924 that give the positions of 2's, 4's and 6's in this sequence, or at least subsets of such positions.

%K nonn

%O 1,3

%A _Antti Karttunen_, Jul 13 2021