

A138241


Number of squares of primes between cubes of successive primes.


1



2, 2, 2, 4, 3, 5, 3, 7, 7, 3, 9, 7, 5, 6, 10, 11, 4, 10, 7, 6, 12, 7, 13, 16, 8, 5, 10, 4, 8, 29, 13, 13, 7, 21, 3, 14, 16, 12, 13, 18, 4, 22, 6, 14, 7, 29, 31, 11, 5, 12, 18, 7, 27, 17, 19, 15, 6, 17, 12, 6, 31, 36, 17, 7, 9, 44, 19, 34, 4, 13, 20, 29, 15, 19, 11, 23, 27, 11, 27, 31, 7, 37
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OFFSET

1,1


COMMENTS

Or, number of terms in A001248 between A030078(n) and A030078(n+1).


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..5000


EXAMPLE

First two cubes of primes: between p(1)^3=8 and p(2)^3=27 there are exactly two squares of primes, 9 and 25, hence a(1)=2. Similarly, between p(2)^3=27 and p(3)^3=125, there are exactly 2 squares of primes, 49 and121, hence a(2)=2. (Typo corrected Jul 01 2008.)
{n,p(n)^3,p(n+1)^3}, (squares of primes)}, a(n)}
n=1: {8,27}, {9,25}, a(n)=2
n=2: {27,125}, {49,121}, a(n)=2
n=3: {125,343}, {169,289}, a(n)=2
n=4: {343,1331}, {361,529,841,961}, a(n)=4
n=5: {1331,2197}, {1369,1681,1849}, a(n)=3
n=6: {2197,4913}, {2209,2809,3481,3721,4489}, a(n)=5
n=7: {4913,6859}, {5041,5329,6241}, a(n)=3
n=8: {6859,12167}, {6889,7921,9409,10201,10609,11449,11881}, a(n)=7
n=9: {12167,24389}, {12769,16129,17161,18769,19321,22201,22801},a(n)=7
n=10: {24389,29791}, {24649,26569,27889}, a(n)=3.


MATHEMATICA

Table[PrimePi[Sqrt[Prime[n + 1]]^3]  PrimePi[Sqrt[Prime[n]]^3], {n, 1, 100}] (* Vincenzo Librandi, Feb 20 2018 *)


PROG

(PARI) A138241(n) = primepi(sqrt(prime(n+1)^3))  primepi(sqrt(prime(n)^3)) \\ Michael B. Porter, Dec 18 2009


CROSSREFS

Cf. A001248 (Squares of primes), A030078 (Cubes of primes).
Sequence in context: A031437 A282561 A237598 * A234615 A029145 A238999
Adjacent sequences: A138238 A138239 A138240 * A138242 A138243 A138244


KEYWORD

nonn


AUTHOR

Zak Seidov, May 17 2008


STATUS

approved



