A343127 - OEIS

A343127

Number of solutions to n = x + y + z in positive integers x,y,z such that (x+y) does not divide any of x*y, y*z, or x*z.

0, 0, 1, 1, 1, 2, 3, 4, 5, 5, 7, 9, 10, 12, 16, 17, 18, 21, 23, 27, 30, 33, 36, 41, 43, 45, 50, 54, 57, 63, 67, 72, 76, 81, 88, 93, 96, 102, 110, 117, 121, 130, 135, 143, 151, 155, 163, 173, 177, 182, 190, 198, 205, 215, 224, 233, 240, 249, 259, 272, 278, 288, 301, 308, 317

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OFFSET

1,6

LINKS

Table of n, a(n) for n=1..65.

FORMULA

a(n) = Sum_{j=1..floor(n/3)} Sum_{i=j..floor((n-j)/2)} (ceiling(i*j/(i+j)) - floor(i*j/(i+j))) * (ceiling((i*(n-i-j))/(n-j)) - floor(i*(n-i-j)/(n-j))) * (ceiling((j*(n-i-j))/(n-i)) - floor(j*(n-i-j)/(n-i))).

MATHEMATICA

Table[Sum[Sum[(Ceiling[i*j/(i + j)] - Floor[i*j/(i + j)]) (Ceiling[(i*(n - i - j))/(n - j)] - Floor[i*(n - i - j)/(n - j)]) (Ceiling[(j*(n - i - j))/(n - i)] - Floor[j*(n - i - j)/(n - i)]), {i, j, Floor[(n - j)/2]}], {j, Floor[n/3]}], {n, 100}]

CROSSREFS

Cf. A005279.

Sequence in context: A267508 A163382 A364019 * A094017 A092762 A017844

Adjacent sequences: A343124 A343125 A343126 * A343128 A343129 A343130

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, Apr 05 2021

STATUS

approved