A346239 Möbius transform of A341512, sigma(n)*A003961(n) - n*sigma(A003961(n)).

0, 1, 2, 10, 2, 33, 4, 74, 44, 55, 2, 278, 4, 115, 116, 490, 2, 613, 4, 498, 242, 169, 6, 1942, 92, 265, 742, 1046, 2, 1591, 6, 3086, 344, 355, 330, 4986, 4, 487, 542, 3570, 2, 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

Offset: 1

Author

Antti Karttunen, Jul 13 2021

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Index entries for primes, gaps between
• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to sigma(n)

Crossrefs

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

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.

Programs

PARI

A003961(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); }; \\ From A003961
A341528(n) = (n*sigma(A003961(n)));
A341529(n) = (sigma(n)*A003961(n));
A341512(n) = (A341529(n)-A341528(n));
A346239(n) = sumdiv(n,d,moebius(n/d)*A341512(d));

Formula

a(n) = Sum_{d|n} A008683(n/d) * A341512(d).

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

a(n) = A347125(n) - A347124(n). - Antti Karttunen, Aug 25 2021