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A308147 Sum of the perimeters of all integer-sided isosceles triangles with perimeter n and prime side lengths. 1
0, 0, 0, 0, 0, 6, 7, 8, 9, 0, 11, 12, 13, 0, 15, 16, 34, 0, 19, 0, 21, 0, 0, 24, 50, 0, 54, 28, 58, 0, 31, 0, 66, 0, 35, 36, 74, 0, 117, 40, 123, 0, 86, 0, 135, 0, 47, 48, 147, 0, 153, 0, 106, 0, 55, 0, 171, 0, 59, 60, 122, 0, 189, 64, 260, 0, 134, 0, 276, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

LINKS

Table of n, a(n) for n=1..70.

Wikipedia, Integer Triangle

FORMULA

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

MATHEMATICA

Table[n*Sum[Sum[(PrimePi[i] - PrimePi[i - 1]) (PrimePi[k] - PrimePi[k - 1]) (PrimePi[n - i - k] - PrimePi[n - i - k - 1]) (KroneckerDelta[i, k] + KroneckerDelta[i, n - i - k] - KroneckerDelta[k, 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. A010051, A070092.

Sequence in context: A198124 A120207 A202703 * A308165 A090928 A199174

Adjacent sequences:  A308144 A308145 A308146 * A308148 A308149 A308150

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, May 14 2019

STATUS

approved

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Last modified January 22 21:47 EST 2022. Contains 350504 sequences. (Running on oeis4.)