A378721 a(n) is the denominator of the asymptotic density of numbers whose third smallest prime divisor is prime(n).

1, 1, 30, 30, 165, 15015, 36465, 62985, 7436429, 11849255, 73465381, 33426748355, 50708377254535, 436092044389001, 1863302371480277, 1086305282573001491, 64092011671807087969, 3909612711980232366109, 8449808119441147371913, 18598027670889965365580513, 3543193335582015099413

Offset

1,3

Comments

See A378720 for more details.

Links

Amiram Eldar, Table of n, a(n) for n = 1..365

Mathematica

a[n_] := Block[{p, q = Prime@ Range@ n}, p = Fold[Times, 1, q]; q = Most@ q; Plus @@ Times @@@ Subsets[q -1, {n -3}]/p]; a[1] = 0; Denominator@ Array[a, 21]

Prog

(PARI) a(n) = {my(v = primes(n), q = vecextract(apply(x -> x-1, v), "^-1"), p = vecprod(v), prd = vecprod(q)/p, sm = 0, sb); forsubset([#q, 2], s, sb = vecextract(q, s); sm += 1/vecprod(sb)); denominator(prd * sm); }

Crossrefs

Cf. A000040, A038110, A038111, A342479, A342480, A378720 (numerators).

Sequence in context: A186902 A185487 A051723 * A247517 A165851 A162503

Adjacent sequences: A378716 A378717 A378720 * A378722 A378723 A378729

Keyword

nonn,easy,frac,new

Author

Robert G. Wilson v and Amiram Eldar, Dec 05 2024

Status

approved