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A120036 Number of 5-almost primes 5ap such that 2^n < 5ap <= 2^(n+1). 8
0, 0, 0, 0, 1, 1, 5, 8, 21, 41, 91, 199, 403, 873, 1767, 3740, 7709, 15910, 32759, 67185, 138063, 281566, 576165, 1173435, 2390366, 4860357, 9873071, 20033969, 40612221, 82266433, 166483857, 336713632, 680482316, 1374413154, 2774347425 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,7

COMMENTS

The partial sum equals the number of Pi_5(2^n) = 0, 0, 0, 0, 1, 2, 7, 15, 36, 77, 168, 367, 770, 1643,..

LINKS

Table of n, a(n) for n=0..34.

EXAMPLE

(2^5, 2^6] there is one semiprime, namely 48. 32 was counted in the previous entry.

MATHEMATICA

FiveAlmostPrimePi[n_] := Sum[ PrimePi[n/(Prime@i*Prime@j*Prime@k*Prime@l)] - l + 1, {i, PrimePi[n^(1/5)]}, {j, i, PrimePi[(n/Prime@i)^(1/4)]}, {k, j, PrimePi[(n/(Prime@i*Prime@j))^(1/3)]}, {l, k, PrimePi[(n/(Prime@i*Prime@j*Prime@k))^(1/2)]}]; t = Table[ FiveAlmostPrimePi[2^n], {n, 0, 37}]; Rest@t - Most@t

CROSSREFS

Cf. A014614, A114453, A036378, A120033, A120034, A120035, A120036, A120037, A120038, A120039, A120040, A120041, A120042, A120043.

Sequence in context: A331700 A105634 A294124 * A036381 A277369 A140419

Adjacent sequences:  A120033 A120034 A120035 * A120037 A120038 A120039

KEYWORD

nonn

AUTHOR

Jonathan Vos Post and Robert G. Wilson v, Mar 20 2006

STATUS

approved

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Last modified January 15 18:55 EST 2021. Contains 340188 sequences. (Running on oeis4.)