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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
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
M. Beeler, R. W. Gosper, and R. Schroeppel, HAKMEM ITEM 45.
Raphael M. Robinson, Multiple tiling of n-dimensional space by unit cubes, Math. Z., Vol. 166 (1979), pp. 225-264.
Chuanming Zong, What is known about unit cubes, Bull. Amer. Math. Soc., Vol. 42, No. 2 (2005), pp. 181-211; Robinson theorem cited on p. 204.
FORMULA
{a(n)} = {j such that for some k>1 A001248(k)|j} = {j such that for some k>0 (A065091(k)^2)|j}. - Jonathan Vos Post, Aug 06 2007
A008966(A000265(a(n))) = 0. - Reinhard Zumkeller, Nov 08 2009
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. A000040, A065091, A122132 (complement).
Cf. A013929 (supersequence of nonsquarefrees).
Subsequences: A001248 \ {2} (primitives), A053850 (odds), A036785 (divisible by the squares of two distinct primes).
Subsequence of A167662. - Reinhard Zumkeller, Nov 08 2009
Sequence in context: A028494 A167663 A347242 * A347247 A038837 A325359
KEYWORD
nonn
STATUS
approved