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

1,5

Comments

No negative terms.

Links

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.

Formula

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.

Prog

(PARI)
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));

Crossrefs

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

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

Sequence in context: A049271 A004178 A068333 * A121451 A265820 A096984

Adjacent sequences: A378745 A378746 A378747 * A378749 A378750 A378751

Keyword

nonn,new

Author

Antti Karttunen, Dec 09 2024

Status

approved