A140114 -id:A140114 - cp's OEIS frontend

A178133 Number of odd semiprimes between consecutive squares.

0, 0, 1, 1, 2, 1, 3, 3, 5, 3, 5, 4, 4, 9, 5, 4, 10, 6, 7, 8, 8, 11, 10, 8, 8, 14, 11, 12, 11, 13, 10, 13, 14, 15, 14, 16, 17, 12, 14, 14, 18, 19, 17, 19, 15, 21, 16, 17, 23, 22, 17, 16, 21, 24, 28, 24, 21, 23, 20, 24, 22, 24, 21, 27, 28, 28, 26, 28, 32, 19, 31, 29, 27, 29, 28, 22, 37

Offset: 1

Vladimir Joseph Stephan Orlovsky, May 20 2010

nonn

Odd squarefree semiprimes: 15, 21, 33, 35, 39, 51, 55, 57, 65, 69, 77, 85, 87, 91, 93, 95, 111,.... Between 1^2 and 2^2 there are no odd squarefree semiprimes, between 2^2 and 3^2 there are no odd squarefree semiprimes, between 3^2 and 4^2 there is one odd squarefree semiprime 15, between 4^2 and 5^2 there is one odd squarefree semiprimes 21, between 5^2 and 6^2 there are two odd squarefree semiprimes 33,35.

T. D. Noe, Table of n, a(n) for n = 1..1000

Cf. A140114 (number of semiprimes between squares), A046388, A188443.

fQ[n_] := OddQ[n] && Last /@ FactorInteger[n] == {1, 1}; f[n_] := Length[Select[ Range[n^2, (n + 1)^2], fQ]]; Array[f, 77] (* Robert G. Wilson v, Jun 07 2011 *)

A140115 a(n) is the number of numbers k between n^3 and (n + 1)^3 that are the product of 3 distinct primes.

Original entry on oeis.org

0, 0, 0, 2, 7, 10, 16, 27, 32, 41, 53, 72, 76, 104, 104, 143, 137, 174, 203, 209, 241, 271, 280, 324, 360, 381, 391, 466, 497, 499, 545, 598, 646, 676, 737, 725, 818, 850, 930, 953, 948, 1055, 1113, 1151, 1221, 1301, 1294, 1394, 1425, 1520, 1589, 1657, 1694, 1766, 1801

Offset: 0

Philippe Lallouet (philip.lallouet(AT)orange.fr), May 08 2008

			a(3) = 2, counting 30 and 42 between 3^3 = 27 and 4^3 = 64.
a(4) = 7, counting 66, 70, 78, 102, 105, 110 and 114 between 4^3 = 64 and 5^3 = 125. - _David A. Corneth_, May 19 2018

Cf. A007304, A140114.

list(lim)=my(v=List(), t); forprime(p=2, (lim)^(1/3), forprime(q=p+1, sqrt(lim\p), t=p*q; forprime(r=q+1, lim\t, listput(v, t*r)))); vecsort(Vec(v)) \\ Charles R Greathouse IV, Jul 20 2011 at A007304.
first(n) = {my(res = vector(n), l = list(n ^ 3), il = 1, ir = 4, ol = nl = 1); res[1] = 0; while(il <= #l, if(ir ^ 3 < l[il], ir++); res[ir]++; il++); res} \\ David A. Corneth, May 19 2018

Corrected name, data and put more terms by David A. Corneth, May 19 2018

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A178133 Number of odd semiprimes between consecutive squares.

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A140115 a(n) is the number of numbers k between n^3 and (n + 1)^3 that are the product of 3 distinct primes.

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