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

Author

Amiram Eldar, Dec 03 2024

Keywords

• nonn
• easy
• frac

Comments

See A378680 for more details.

Links

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

Crossrefs

Cf. A087039, A087040, A378680 (numerators).

Programs

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]}]]

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), ", "));}