A211484 Numbers n for which the canonical prime factorization contains only an even number of exponents, all of which are congruent to 1 modulo 3.

1, 6, 10, 14, 15, 21, 22, 26, 33, 34, 35, 38, 39, 46, 48, 51, 55, 57, 58, 62, 65, 69, 74, 77, 80, 82, 85, 86, 87, 91, 93, 94, 95, 106, 111, 112, 115, 118, 119, 122, 123, 129, 133, 134, 141, 142, 143, 145, 146, 155, 158, 159, 161, 162, 166, 176, 177, 178, 183

Offset

1,2

Comments

By convention 1 is included as the first term, in order to simplify the statement of certain results involving this sequence.

Links

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

Example

6 is included, as its canonical prime factorization  (2^1)*(3^1) contains an even number of exponents, all of which are congruent to 1 modulo 3.

Mathematica

pfQ[n_]:=Module[{f=Transpose[FactorInteger[n]][[2]]}, EvenQ[Length[f]] && Union[ Mod[f, 3]]=={1}]; Join[{1}, Select[Range[200], pfQ]] (* Harvey P. Dale, Mar 24 2016 *)

Prog

(PARI) {plnt=1; k=1; print1(k, ", "); plnt++;
mxind=76 ; mxind++ ; for(k=2, 10^6,
M=factor(k); passes=1;
sz = matsize(M)[1];
for(k=1, sz, if(sz%2 != 0, passes=0; break()); if( M[k, 2] % 3 != 1, passes=0));
if( passes == 1 , print1(k, ", "); plnt++) ; if(mxind ==  plnt, break() ))}
(PARI) is(n, f=factor(n))=omega(f)%2==0 && factorback(f[, 2]%3)==1 \\ Charles R Greathouse IV, Sep 07 2017

Crossrefs

This sequence includes A030229 and hence A006881. The definition is similar to that for A211485.

Sequence in context: A367590 A268390 A265693 * A339561 A350486 A346014

Adjacent sequences: A211481 A211482 A211483 * A211485 A211486 A211487

Keyword

nonn,easy

Author

Douglas Latimer, Apr 12 2012

Status

approved