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A086670 Sum of floor(d/2) where d is a divisor of n. 1
0, 1, 1, 3, 2, 5, 3, 7, 5, 8, 5, 13, 6, 11, 10, 15, 8, 18, 9, 20, 14, 17, 11, 29, 14, 20, 18, 27, 14, 34, 15, 31, 22, 26, 22, 44, 18, 29, 26, 44, 20, 46, 21, 41, 36, 35, 23, 61, 27, 45, 34, 48, 26, 58, 34, 59, 38, 44, 29, 82, 30, 47, 49, 63, 40, 70, 33, 62, 46, 70, 35, 96, 36, 56 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Inverse Mobius transform of A004526. - R. J. Mathar, Jan 19 2009

LINKS

Table of n, a(n) for n=1..74.

FORMULA

G.f.: Sum_{n>=1} floor(n/2)*x^n/(1-x^n). - Joerg Arndt, Jan 30 2011

a(n) = (A000203(n) - A001227(n)) / 2. - Franklin T. Adams-Watters, Jan 05 2012

G.f.: Sum_{k>=1} x^(2*k) / ((1 + x^k) * (1 - x^k)^2). - Ilya Gutkovskiy, Aug 02 2021

a(n) = Sum_{i=1..floor(n/2)} A135539(n,2*i). - Ridouane Oudra, Apr 15 2022

EXAMPLE

10 has divisors 1,2,5,10. floor(d/2) gives 0,1,2,5, therefore a(10)=8.

PROG

(PARI) for (n=1, 100, s=0; fordiv(i=n, i, s+=floor(i/2)); print1(", "s))

(PARI) a(n) = my(f = factor(n)); (sigma(f) - (numdiv(f)/(valuation(n, 2)+1)))>>1 \\ David A. Corneth, Apr 15 2022 using Franklin T. Adams-Watters's formula

CROSSREFS

Cf. A000203, A001227, A004526, A079247.

Cf. A135539.

Sequence in context: A083242 A111618 A107128 * A075888 A075889 A181771

Adjacent sequences: A086667 A086668 A086669 * A086671 A086672 A086673

KEYWORD

nonn

AUTHOR

Jon Perry, Jul 27 2003

STATUS

approved

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Last modified December 7 10:26 EST 2022. Contains 358656 sequences. (Running on oeis4.)