A387409 Partial sums of A387422 minus partial sums of A387412.

0, 0, 0, -2, -2, -1, -1, -1, -1, -3, -3, -2, -1, 0, 1, 0, 0, -1, -1, 2, 3, 3, 3, 4, 2, 0, -1, 2, 2, 1, 1, 1, -3, -3, -5, -4, -2, -4, -5, -5, -5, -8, -8, -6, -7, -8, -8, -10, -10, -10, -10, -8, -6, -5, -5, -3, -8, -8, -8, -8, -5, -5, -4, -5, -4, -2, -2, -3, -5, -3, -3, -4, -3, -3, -3, -1, -3, -2, -2, -1, -2, -3, -2

Offset: 1

Author

Antti Karttunen, Sep 03 2025

Keywords

• sign
• base
• new

Comments

Also partial sums of A387413 minus partial sums of A387423.

This sequence gives some measure of how much longer the common prefix of the binary expansions of n and sigma(n) is - on average - than the common prefix of the binary expansions of n and A003961(n).

Question: Does the sequence eventually grow without limit and is it just because A003961(n) >= A000203(n)? Does ratio a(n)/n converge to any limit?

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• A. Karttunen, Ratio a(n)/n, plotted with OEIS Plot2-tool
• Index entries for sequences related to binary expansion of n.
• Index entries for sequences related to prime indices in the factorization of n.
• Index entries for sequences related to sigma(n).

Crossrefs

Cf. A000203, A003961, A387407, A387408, A387412, A387413, A387422, A387423, A387424, A387425.

Programs

PARI

A387409(n) = (A387407(n) - A387408(n));

Formula

a(n) = A387407(n) - A387408(n).

a(n) = A387425(n) - A387424(n).