

A038838


Numbers that are divisible by the square of an odd prime.


25



9, 18, 25, 27, 36, 45, 49, 50, 54, 63, 72, 75, 81, 90, 98, 99, 100, 108, 117, 121, 125, 126, 135, 144, 147, 150, 153, 162, 169, 171, 175, 180, 189, 196, 198, 200, 207, 216, 225, 234, 242, 243, 245, 250, 252, 261, 270, 275, 279, 288, 289, 294, 297, 300, 306
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OFFSET

1,1


COMMENTS

Condition 1 of Theorem 7.5 (Robinson, 1979) includes: "k is a multiple of a square of an odd prime."  Jonathan Vos Post, Aug 06 2007
If m is a term, every k*m with k > 1 is another term and the primitive terms are the square of odd primes. The subsequence of odd terms is A053850 while the even terms 18, 36, 50, 54, 72, 90, 98, ... are exactly twice the terms of this sequence.  Bernard Schott, Nov 20 2020
The asymptotic density of this sequence is 1  8/Pi^2 = 0.189430...  Amiram Eldar, Nov 21 2020


LINKS



FORMULA



PROG

(PARI) {a(n) = my(m, c); if( n<1, 0, c=0; m=0; while( c<n, m++; if( moebius(m / 2^valuation(m, 2))==0, c++)); m)}; /* Michael Somos, Aug 22 2006 */
(PARI) list(lim)=my(v=List(), n, e, t); forfactored(k=9, lim\1, e=k[2][, 2]; t=#e; n=k[1]; if(if(n%2 && t, vecmax(e)>1, t>1, vecmax(e[2..t])>1, 0), listput(v, k[1]))); Vec(v) \\ Charles R Greathouse IV, Jan 08 2018


CROSSREFS

Cf. A013929 (supersequence of nonsquarefrees).
Subsequences: A001248 \ {2} (primitives), A053850 (odds), A036785 (divisible by the squares of two distinct primes).


KEYWORD

nonn


AUTHOR



STATUS

approved



