A038838 - OEIS (original) (raw)

A038838

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

29

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

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

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).