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A308450 Number of integer-sided triangles with perimeter n whose smallest side length is prime. 4
0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 3, 2, 3, 2, 4, 3, 5, 4, 6, 4, 7, 5, 8, 6, 9, 7, 10, 7, 10, 7, 10, 7, 11, 8, 12, 9, 13, 10, 15, 12, 17, 14, 19, 15, 20, 16, 21, 17, 22, 18, 24, 19, 25, 20, 26, 21, 28, 23, 30, 25, 32, 27, 34, 29, 36, 31, 38, 32, 40, 34, 42, 36 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,9

LINKS

Table of n, a(n) for n=1..72.

FORMULA

a(n) = Sum_{k=1..floor(n/3)} Sum_{i=k..floor((n-k)/2)} sign(floor((i+k)/(n-i-k+1))) * c(k), where c(n) is the prime characteristic (A010051).

MATHEMATICA

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

CROSSREFS

Cf. A010051.

Sequence in context: A060129 A327161 A350067 * A229123 A173908 A329045

Adjacent sequences: A308447 A308448 A308449 * A308451 A308452 A308453

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, May 27 2019

STATUS

approved

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Last modified January 28 14:10 EST 2023. Contains 359895 sequences. (Running on oeis4.)