

A182120


Numbers n for which the canonical prime factorization contains only exponents which are congruent to 2 modulo 3.


1



1, 4, 9, 25, 32, 36, 49, 100, 121, 169, 196, 225, 243, 256, 288, 289, 361, 441, 484, 529, 676, 800, 841, 900, 961, 972, 1089, 1156, 1225, 1369, 1444, 1521, 1568, 1681, 1764, 1849, 2048, 2116, 2209, 2304, 2601, 2809, 3025, 3125, 3249, 3364, 3481, 3721, 3844
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OFFSET

1,2


COMMENTS

By convention 1 is included as the first term.


LINKS

Douglas Latimer, Table of n, a(n) for n = 1..1000


EXAMPLE

100 is included, as its canonical prime factorization (2^2)*(5^2) contains only exponents which are congruent to 2 modulo 3.


MATHEMATICA

Join[{1}, Select[Range[5000], Union[Mod[Transpose[FactorInteger[#]][[2]], 3]] == {2}&]] (* Harvey P. Dale, Aug 18 2014 *)


PROG

(PARI) {plnt=1; k=1; print1(k, ", "); plnt++;
mxind=76 ; mxind++ ; for(k=2, 2*10^6,
M=factor(k); passes=1;
sz = matsize(M)[1];
for(k=1, sz, if( M[k, 2] % 3 != 2, passes=0));
if( passes == 1 ,
print1(k, ", "); plnt++) ; if(mxind == plnt, break() ))}


CROSSREFS

Includes A000290.
Sequence in context: A232241 A163836 A175085 * A099998 A030140 A153158
Adjacent sequences: A182117 A182118 A182119 * A182121 A182122 A182123


KEYWORD

nonn,easy


AUTHOR

Douglas Latimer, Apr 12 2012


STATUS

approved



