A395569 Moebius transform of A396683 = d(A006863), where d = A000005 is the divisor function.

8, 12, 16, 4, 8, 84, 0, 32, 40, 32, 8, 20, 0, 20, 64, 8, 0, 480, 0, 80, 48, 12, 8, 160, 0, 20, 16, 4, 8, 1216, 0, 8, 64, 0, 16, 872, 0, 0, 24, 160, 8, 532, 0, 52, 120, 12, 0, 424, 0, 100, 24, 4, 8, 944, 24, 144, 0, 12, 0, 1912, 0, 0, 272, 8, 16, 276, 0, 24, 64, 144, 0, 1856, 0

Offset

1,1

Comments

For n > 1, number of k such that psi(k) = 2*n.

Links

Jianing Song, Table of n, a(n) for n = 1..10000

Example

There are a(2) = 12 values of k such that psi(k) = 4: k = 5, 10, 15, 16, 20, 30, 40, 48, 60, 80, 120, 240.
There are a(3) = 16 values of k such that psi(k) = 6: k = 7, 9, 14, 18, 21, 28, 36, 42, 56, 63, 72, 84, 126, 168, 252, 504.
There are a(4) = 4 values of k such that psi(k) = 8: k = 32, 96, 160, 480.
a(7) = 0 since 14 is not in A002174, the range of psi.

Prog

(PARI) a(n) = sumdiv(n, d, moebius(n/d) * numdiv(A079612(2*d))) \\ See A079612 for its program

Crossrefs

Cf. A006863, A000005, A002322, A396683.

Cf. also A143408, A396684 (indices of nonzero terms), A396685 (indices of zeros), A002174.

Sequence in context: A287373 A031034 A152758 * A160258 A071280 A033942

Adjacent sequences: A395566 A395567 A395568 * A395570 A395571 A395572

Keyword

nonn,easy

Author

Jianing Song, Jun 02 2026

Status

approved