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This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A378819 a(n) is the number of distinct nondegenerate triangles whose sides are prime factors of n.

Original entry on oeis.org

0, 1, 1, 1, 1, 4, 1, 1, 1, 3, 1, 4, 1, 3, 4, 1, 1, 4, 1, 3, 3, 3, 1, 4, 1, 3, 1, 3, 1, 8, 1, 1, 3, 3, 4, 4, 1, 3, 3, 3, 1, 7, 1, 3, 4, 3, 1, 4, 1, 3, 3, 3, 1, 4, 3, 3, 3, 3, 1, 8, 1, 3, 3, 1, 3, 7, 1, 3, 3, 7, 1, 4, 1, 3, 4, 3, 4, 7, 1, 3, 1, 3, 1, 7, 3, 3, 3, 3
Offset: 1

Views

Author

Felix Huber, Dec 27 2024

Keywords

Comments

A prime factor can be used for several sides.
A nondegenerate triangle is a triangle whose sides (u, v, w) are such that u + v > w, v + w > u and u + w > v.

Examples

			a(10) = 3 because there are the 3 distinct nondegenerate triangles (2, 2, 2), (2, 5, 5), (5, 5, 5) whose sides are prime factors of 10. Since 2 + 2 < 5, (2, 2, 5) is not a triangle.

Links

Crossrefs

Cf. A000040, A000961, A001221, A007947, A070088, A306678, A316841, A316842, A366398, A378820, A379033.

Programs

  • Maple
    A378819:=proc(n)
   local a,i,j,k,L;
   L:=NumberTheory:-PrimeFactors(n);
   a:=0;
   for i to nops(L) do
      for j from i to nops(L) do
         for k from j to nops(L) while L[k]A378819(n),n=1..88);

Formula

a(n) = a(A007947(n)).
a(p^k) = 1 for prime powers p^k (p prime, k >= 1).

A386417 Numbers k for which there exists at least one nondegenerate triangle with sides that are distinct divisors of k.

Original entry on oeis.org

12, 20, 24, 30, 36, 40, 42, 48, 56, 60, 63, 70, 72, 80, 84, 88, 90, 96, 99, 100, 105, 108, 110, 112, 120, 126, 130, 132, 140, 144, 150, 154, 156, 160, 165, 168, 176, 180, 182, 189, 192, 195, 198, 200, 204, 208, 210, 216, 220, 224, 228, 234, 238, 240, 252, 255, 260
Offset: 1

Views

Author

Felix Huber, Jul 28 2025

Keywords

Comments

If k is a term, then m*k is also a term for all positive integers m.

Examples

			12 is a term because the sides of the nondegenerate triangles (2, 3, 4) and (3, 4, 6) are divisors of 12.

Links

Crossrefs

Cf. A027750, A378820, A386418.

Programs

  • Maple
    A386417:=proc(n)
    option remember;
    local k,i;
    if n=1 then
        12
    else
        for k from procname(n-1)+1 do
            for i in combinat[choose](NumberTheory:-Divisors(k),3) do
                if i[3]A386417(n),n=1..25);

A386418 a(n) is the number of nondegenerate triangles whose sides are distinct divisors of A386417(n).

Original entry on oeis.org

2, 1, 5, 4, 6, 4, 2, 8, 3, 23, 1, 3, 19, 8, 14, 1, 17, 11, 1, 2, 3, 10, 2, 7, 57, 14, 1, 11, 13, 37, 9, 2, 8, 12, 1, 45, 4, 79, 3, 3, 14, 2, 7, 9, 5, 3, 45, 35, 11, 12, 4, 6, 1, 106, 62, 2, 8, 33, 1, 34, 3, 4, 41, 1, 3, 57, 4, 3, 50, 2, 6, 7, 25, 12, 16, 14, 30
Offset: 1

Views

Author

Felix Huber, Jul 28 2025

Keywords

Examples

			a(1) = 2 because there are exactly the 2 triangles (2, 3, 4) and (3, 4, 6) whose sides are distinct divisors of A386417(1) = 12.

Links

Crossrefs

Cf. A027750, A378820, A386417.

Programs

  • Maple
    A386418:=proc(n)
    option remember;
    local a,k,i;
    if n=1 then
        [12,2]
    else
        for k from procname(n-1)[1]+1 do
            a:=0;
            for i in combinat[choose](NumberTheory:-Divisors(k),3) do
                if i[3]0 then
                return [k,a]
            fi
        od
    fi;
end proc;
seq(A386417(n)[2],n=1..77);
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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