A378521 -id:A378521 - cp's OEIS frontend

A378748 Möbius transform of A378747.

1, 0, 1, 1, 2, 0, 4, 5, 7, 0, 5, 4, 7, 2, 5, 19, 8, 8, 10, 6, 11, 0, 13, 20, 16, 2, 41, 14, 14, 2, 17, 65, 11, 0, 19, 36, 19, 2, 17, 30, 20, 10, 22, 12, 39, 4, 25, 76, 48, 12, 17, 20, 28, 64, 21, 58, 23, 0, 29, 28, 32, 4, 73, 211, 31, 2, 34, 18, 31, 14, 35, 132, 38, 2, 49, 26, 43, 10, 40, 114, 223, 0, 43, 60, 33, 2

Offset: 1

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Antti Karttunen, Dec 09 2024

nonn

No negative terms.

Antti Karttunen, Table of n, a(n) for n = 1..20000
Index entries for sequences related to prime indices in the factorization of n.
Index entries for primes, gaps between.

Cf. A000010, A003961, A003972, A008683, A048673, A051953, A378521, A378747.

Positions of 0's is given by {2} U A108605.

A048673(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); (factorback(f)+1)/2; };
A378747(n) = (A048673(n)-(sigma(n)-n));
A378748(n) = sumdiv(n,d,moebius(d)*A378747(n/d));

a(n) = Sum_{d|n} A008683(d)*A378747(n/d).
a(n) = A378521(n) - A051953(n).
For n > 1, a(n) = A000010(n) + A000010(A003961(n))/2 - n.

cp's OEIS Frontend

A378748 Möbius transform of A378747.

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