A378681 a(n) = denominator(Sum_{k=1..n} 1/P_2(k)), where P_2(k) = A087040(k) is the second largest prime dividing the k-th composite number.

2, 1, 2, 6, 3, 6, 3, 3, 6, 2, 1, 3, 6, 3, 15, 30, 30, 15, 5, 10, 30, 15, 15, 15, 30, 10, 5, 15, 30, 30, 15, 30, 210, 210, 70, 35, 105, 105, 210, 210, 105, 35, 70, 210, 105, 21, 21, 42, 14, 70, 210, 105, 105, 210, 210, 210, 105, 35, 70, 210, 210, 105, 105, 210

Offset

1,1

Comments

See A378680 for more details.

Links

Amiram Eldar, Table of n, a(n) for n = 1..1000

Mathematica

p2[c_] := Module[{f = FactorInteger[c]}, If[f[[-1, 2]] > 1, f[[-1, 1]], f[[-2, 1]]]]; Denominator@ Accumulate[Table[1/p2[c], {c, Select[Range[50], CompositeQ]}]]

Prog

(PARI) lista(nmax) = {my(s = 0); forcomposite(n = 1, nmax, f = factor(n); s += if(f[#f~, 2] > 1, 1/f[#f~, 1], 1/f[#f~ - 1, 1]); print1(denominator(s), ", ")); }

Crossrefs

Cf. A087039, A087040, A378680 (numerators).

Sequence in context: A099206 A269223 A121341 * A241737 A174959 A126093

Adjacent sequences: A378678 A378679 A378680 * A378685 A378686 A378687

Keyword

nonn,easy,frac,new

Author

Amiram Eldar, Dec 03 2024

Status

approved