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 A215218 Number of sphenic numbers, i.e., numbers with exactly three distinct prime factors, up to 10^n. 6
 0, 5, 135, 1800, 19919, 206964, 2086746, 20710806, 203834084, 1997171674, 19522428788, 190614467420, 1860310801454, 18155356377267, 177224592578839, 1730651760050923, 16908343191198752, 165279853754232019, 1616504757072680964 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Table of n, a(n) for n=1..19. Paul Kinlaw, Lower bounds for numbers with three prime factors, Husson University, Bangor, ME, 2019. Also in Integers (2019) 19, Article #A22. EXAMPLE a(2) = 5 since there are the five sphenic numbers 30, 42, 66, 70, 78 up to 100. MATHEMATICA f[n_] := Sum[ PrimePi[n/(Prime@ i*Prime@ j)] - j, {i, PrimePi[n^(1/3)]}, {j, i +1, PrimePi@ Sqrt[n/Prime@ i]}]; (* Robert G. Wilson v, Dec 28 2016 *) PROG (Python) from math import isqrt from sympy import primepi, primerange, integer_nthroot def A215218(n): return int(sum(primepi(10**n//(k*m))-b for a, k in enumerate(primerange(integer_nthroot(10**n, 3)[0]+1), 1) for b, m in enumerate(primerange(k+1, isqrt(10**n//k)+1), a+1))) # Chai Wah Wu, Aug 26 2024 CROSSREFS Cf. A007304. Sequence in context: A085506 A307084 A132508 * A159355 A184577 A229772 Adjacent sequences: A215215 A215216 A215217 * A215219 A215220 A215221 KEYWORD nonn AUTHOR Martin Renner, Aug 06 2012 EXTENSIONS a(8)-a(19) from Henri Lifchitz, Nov 11 2012 STATUS approved

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Last modified September 18 23:40 EDT 2024. Contains 376002 sequences. (Running on oeis4.)