A378721 - OEIS

%I #11 Dec 06 2024 11:30:15

%S 1,1,30,30,165,15015,36465,62985,7436429,11849255,73465381,

%T 33426748355,50708377254535,436092044389001,1863302371480277,

%U 1086305282573001491,64092011671807087969,3909612711980232366109,8449808119441147371913,18598027670889965365580513,3543193335582015099413

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

%C See A378720 for more details.

%H Amiram Eldar, <a href="/A378721/b378721.txt">Table of n, a(n) for n = 1..365</a>

%t 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]

%o (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);}

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

%K nonn,easy,frac

%O 1,3

%A _Robert G. Wilson v_ and _Amiram Eldar_, Dec 05 2024