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A241534 Number of integer arithmetic means of 2 distinct divisors of n. 1
0, 0, 1, 1, 1, 2, 1, 3, 3, 2, 1, 7, 1, 2, 6, 6, 1, 6, 1, 7, 6, 2, 1, 16, 3, 2, 6, 7, 1, 12, 1, 10, 6, 2, 6, 18, 1, 2, 6, 16, 1, 12, 1, 7, 15, 2, 1, 29, 3, 6, 6, 7, 1, 12, 6, 16, 6, 2, 1, 34, 1, 2, 15, 15, 6, 12, 1, 7, 6, 12, 1, 39, 1, 2, 15, 7, 6, 12, 1, 29 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

LINKS

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

FORMULA

a(n) = Sum_{d1|n, d2|n, d1 < d2} (1 - ceiling((d1+d2)/2) + floor((d1+d2)/2)). - Wesley Ivan Hurt, Oct 06 2020

EXAMPLE

Triangle T(n, k) starts for n > 2:

2,

3,

3,

2, 4,

4,

3, 5, 6,

2, 5, 6;

where T(n, k) = the values of k such that 2k = q + g; q, g are distinct divisors of n.

a(20) = 7 because (1,5), (2,4), (2,10), (2,20), (4,10), (4,20) and (10,20) are the 7 values of (g,q) such that (g+q)/2 is an integer. - Colin Barker, May 10 2014

MATHEMATICA

Table[Sum[Sum[(1 - Ceiling[(i + k)/2] + Floor[(i + k)/2]) (1 - Ceiling[n/k] + Floor[n/k]) (1 - Ceiling[n/i] + Floor[n/i]), {i, k - 1}], {k, n}], {n, 100}] (* Wesley Ivan Hurt, Oct 06 2020 *)

PROG

(PARI) a(n) = c=0; fordiv(n, g, fordiv(n, q, if(g<q && (g+q)%2==0, c++))); c \\ Colin Barker, May 10 2014

CROSSREFS

Cf. A027750.

Sequence in context: A047679 A179480 A245326 * A337137 A035050 A198790

Adjacent sequences:  A241531 A241532 A241533 * A241535 A241536 A241537

KEYWORD

nonn

AUTHOR

Ilya Lopatin and Juri-Stepan Gerasimov, May 08 2014

EXTENSIONS

Several incorrect terms corrected, and more terms added by Colin Barker, May 10 2014

STATUS

approved

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Last modified December 5 11:56 EST 2021. Contains 349557 sequences. (Running on oeis4.)