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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 21 19:50 EST 2018. Contains 299423 sequences. (Running on oeis4.)