A318878 - OEIS

A318878

Sum of A083254(d) for all such divisors d of n for which A083254(d) > 0.

1, 1, 2, 1, 4, 2, 6, 1, 5, 4, 10, 2, 12, 6, 6, 1, 16, 5, 18, 4, 10, 10, 22, 2, 19, 12, 14, 6, 28, 6, 30, 1, 18, 16, 22, 5, 36, 18, 22, 4, 40, 10, 42, 10, 12, 22, 46, 2, 41, 19, 30, 12, 52, 14, 38, 6, 34, 28, 58, 6, 60, 30, 22, 1, 46, 18, 66, 16, 42, 22, 70, 5, 72, 36, 26, 18, 58, 22, 78, 4, 41, 40, 82, 10, 62, 42, 54, 10, 88, 12, 70, 22, 58, 46, 70, 2

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OFFSET

1,3

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..65537

FORMULA

a(n) = Sum_{d|n} [A083254(d) > 0]*A083254(d), where A083254(n) = 2*phi(n) - n, and [ ] are the Iverson brackets.

a(n) = A318879(n) + A033879(n).

EXAMPLE

n = 105 has divisors [1, 3, 5, 7, 15, 21, 35, 105]. When A083254 is applied to them, we obtain [1, 1, 3, 5, 1, 3, 13, -9]. Summing the positive numbers present, we get a(105) = 1+1+3+5+1+3+13 = 27.

PROG

(PARI) A318878(n) = sumdiv(n, d, d=(2*eulerphi(d))-d; (d>0)*d);

CROSSREFS

Cf. A000010, A033879, A083254, A318879.

Cf. also A318678, A318874, A318876.

Sequence in context: A082729 A326069 A326068 * A306408 A232626 A375124

Adjacent sequences: A318875 A318876 A318877 * A318879 A318880 A318881

KEYWORD

nonn

AUTHOR

Antti Karttunen, Sep 05 2018

STATUS

approved