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A333948 Number of integer-sided triangles with perimeter n whose side lengths have the same number of divisors. 0
0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 2, 1, 0, 2, 1, 2, 1, 1, 1, 1, 3, 1, 3, 2, 2, 4, 2, 3, 3, 4, 1, 3, 2, 5, 4, 4, 2, 6, 2, 5, 2, 6, 3, 6, 2, 6, 4, 7, 5, 7, 4, 6, 5, 6, 6, 8, 7, 9, 5, 5, 5, 11, 5, 9, 3, 8, 8, 13, 8, 10, 6, 6, 9, 15, 13, 13, 10, 15, 12, 16, 14, 17, 10 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,12

LINKS

Table of n, a(n) for n=1..84.

Wikipedia, Integer Triangle

FORMULA

a(n) = Sum_{k=1..floor(n/3)} Sum_{i=k..floor((n-k)/2)} sign(floor((i+k)/(n-i-k+1))) * [d(k) = d(i) = d(n-i-k)], where [] is the Iverson bracket and d(n) is the number of divisors of n (A000005).

EXAMPLE

a(12) = 2; The perimeter of each of the two triangles [2,5,5] and [4,4,4] is 12 and the side lengths for each triangle share the same number of divisors (i.e., d(2) = d(5) = d(5) = 2 and d(4) = d(4) = d(4) = 3).

a(15) = 2; The perimeter of each of the two triangles [3,5,7] and [5,5,5] is 15 and the side lengths for each triangle share the same number of divisors (i.e., d(3) = d(5) = d(7) = 2 and d(5) = d(5) = d(5) = 2).

MATHEMATICA

Table[Sum[Sum[KroneckerDelta[DivisorSigma[0, i], DivisorSigma[0, k], DivisorSigma[0, n - i - k]]*Sign[Floor[(i + k)/(n - i - k + 1)]], {i, k, Floor[(n - k)/2]}], {k, Floor[n/3]}], {n, 100}]

CROSSREFS

Cf. A000005, A005044.

Sequence in context: A236459 A190427 A287108 * A287360 A035443 A180430

Adjacent sequences:  A333945 A333946 A333947 * A333949 A333950 A333951

KEYWORD

nonn,easy

AUTHOR

Wesley Ivan Hurt, Apr 14 2020

STATUS

approved

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Last modified July 28 10:51 EDT 2021. Contains 346326 sequences. (Running on oeis4.)