A324654 a(n) = A033879(A276086(n)).

1, 1, 2, 0, 5, -3, 4, 2, 6, -12, 12, -54, 19, 7, 26, -72, 47, -309, 94, 32, 126, -372, 222, -1584, 469, 157, 626, -1872, 1097, -7959, 6, 4, 10, -12, 22, -60, 22, -4, 18, -156, 6, -612, 102, -44, 58, -876, -74, -3372, 502, -244, 258, -4476, -474, -17172, 2502, -1244, 1258, -22476, -2474, -86172, 41, 25, 66, -96, 141, -459, 148, -46, 102

Offset: 0

Author

Antti Karttunen, Mar 10 2019

Keywords

• sign

Comments

Interestingly, this kind of sampling of deficiency (A033879; recall that the range of A276086 does not cover the whole N) biases it strongly towards negative values: of the first 2310 terms, 1565 are negative (~ 68%) and of the first 30030 terms, 22507 are negative (~ 75%). Compare also to A323174, which covers whole N.

Links

• Antti Karttunen, Table of n, a(n) for n = 0..2310
• Index entries for sequences related to primorial base
• Index entries for sequences related to primorial numbers
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A033879, A276086, A324653.

Cf. also A323174, A324055.

Programs

PARI

A276086(n) = { my(i=0,m=1,pr=1,nextpr); while((n>0),i=i+1; nextpr = prime(i)*pr; if((n%nextpr),m*=(prime(i)^((n%nextpr)/pr));n-=(n%nextpr));pr=nextpr); m; };
A033879(n) = (2*n-sigma(n));
A324654(n) = A033879(A276086(n));

Formula

a(n) = A033879(A276086(n)).

a(n) = 2*A276086(n) - A324653(n).