A378747 a(n) = A048673(n) - A001065(n).

1, 1, 2, 2, 3, 2, 5, 7, 9, 3, 6, 7, 8, 7, 9, 26, 9, 17, 11, 10, 17, 6, 14, 32, 19, 10, 50, 22, 15, 11, 18, 91, 18, 9, 26, 58, 20, 13, 26, 45, 21, 29, 23, 19, 55, 18, 26, 127, 53, 31, 27, 31, 29, 122, 29, 85, 35, 15, 30, 50, 33, 22, 97, 302, 41, 20, 35, 28, 46, 42, 36, 215, 39, 22, 74, 40, 53, 38, 41, 178, 273, 21

Offset: 1

Author

Antti Karttunen, Dec 09 2024

Keywords

• nonn

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.

Crossrefs

Cf. A000203, A001065, A003961, A048673, A337378 (where a(n) > n), A337379 (where a(n) <= n), A378748 (Möbius transform), A378749 (Dirichlet inverse).

Cf. also A286385, A349573.

Programs

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));

Formula

a(n) = n + (A003961(n)+1)/2 - A000203(n).