A098719 Position of prime(n)# in A025487.

1, 2, 4, 9, 22, 54, 114, 246, 488, 948, 1809, 3327, 6020, 10624, 18246, 30726, 51148, 84074, 135598, 216398, 340886, 529051, 814237, 1240172, 1874464, 2817289, 4195918, 6186286, 9049492, 13121704, 18895821, 27199504, 38892092, 55318849, 78130780, 110028527

Offset

1,2

Links

Chai Wah Wu, Table of n, a(n) for n = 1..67

Mathematica

Block[{nn = 24, f, s}, f[n_] := {{1}}~Join~Block[{lim = Product[Prime@ i, {i, n}], ww = NestList[Append[#, 1] &, {1}, n - 1], g}, g[x_] := Apply[Times, MapIndexed[Prime[First@ #2]^#1 &, x]]; Map[Block[{w = #, k = 1}, Sort@ Prepend[If[Length@ # == 0, #, #[[1]]], Product[Prime@ i, {i, Length@ w}]] &@ Reap[Do[If[# < lim, Sow[#]; k = 1, If[k >= Length@ w, Break[], k++]] &@ g@ Set[w, If[k == 1, MapAt[# + 1 &, w, k], PadLeft[#, Length@ w, First@ #] &@ Drop[MapAt[# + Boole[i > 1] &, w, k], k - 1]]], {i, Infinity}]][[-1]]] &, ww]]; s = Sort[Join @@ f@ nn]; {1}~Join~Array[Position[s, Product[Prime@ i, {i, #}]] &, nn][[All, 1, 1]]] (* Michael De Vlieger, Jul 23 2018 *)

Prog

(Python)
from functools import lru_cache
from sympy import prime, integer_log, primorial
def A098719(n):
    @lru_cache(maxsize=None)
    def g(x, m, j): return sum(g(x//(prime(m)**i), m-1, i) for i in range(j, integer_log(x, prime(m))[0]+1)) if m-1 else max(0, x.bit_length()-j)
    return 1+sum(g(primorial(n-1), k, 1) for k in range(1, n)) # Chai Wah Wu, Mar 23 2026

Crossrefs

Cf. A002110, A025487.

Sequence in context: A317735 A238826 A048211 * A274289 A265023 A343291

Adjacent sequences: A098716 A098717 A098718 * A098720 A098721 A098722

Keyword

nonn

Author

Jeff Burch, Sep 29 2004

Extensions

Extended by T. D. Noe, Nov 12 2010

More terms from Michael De Vlieger, Jul 23 2018

Name corrected by Amiram Eldar, Jun 05 2022

Status

approved