

A205402


Least k such that n divides s(k)s(j) for some j < k, where s(j) = floor((j+1)^2/2)/2 (quartersquares).


9



2, 3, 3, 4, 4, 6, 5, 5, 8, 6, 6, 7, 9, 7, 7, 8, 11, 8, 8, 11, 9, 12, 9, 9, 14, 10, 11, 10, 10, 11, 14, 11, 12, 11, 11, 12, 13, 12, 15, 12, 12, 16, 13, 14, 13, 20, 13, 13, 19, 14, 17, 14, 20, 14, 14, 16, 21, 15, 25, 15, 17, 15, 15, 19, 17, 16, 28, 16, 17, 16, 16, 17, 26
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OFFSET

1,1


COMMENTS

See A204892 for a discussion and guide to related sequences.


LINKS



MATHEMATICA

s[n_] := s[n] = (1/2) Floor[(n + 1)^2/2];
z1 = 1000; z2 = 80;
Table[s[n], {n, 1, 30}] (* A002620, quartersquares *)
u[m_] := u[m] = Flatten[Table[s[k]  s[j], {k, 2, z1}, {j, 1, k  1}]][[m]]
Table[u[m], {m, 1, z1}] (* A205400 *)
v[n_, h_] := v[n, h] = If[IntegerQ[u[h]/n], h, 0]
w[n_] := w[n] = Table[v[n, h], {h, 1, z1}]
d[n_] := d[n] = First[Delete[w[n], Position[w[n], 0]]]
Table[d[n], {n, 1, z2}] (* A205401 *)
k[n_] := k[n] = Floor[(3 + Sqrt[8 d[n]  1])/2]
m[n_] := m[n] = Floor[(1 + Sqrt[8 n  7])/2]
j[n_] := j[n] = d[n]  m[d[n]] (m[d[n]] + 1)/2
Table[k[n], {n, 1, z2}] (* A205402 *)
Table[j[n], {n, 1, z2}] (* A205403 *)
Table[s[k[n]], {n, 1, z2}] (* A205404 *)
Table[s[j[n]], {n, 1, z2}] (* A205405 *)
Table[s[k[n]]  s[j[n]], {n, 1, z2}] (* A205406 *)
Table[(s[k[n]]  s[j[n]])/n, {n, 1, z2}] (* A198293 *)


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



