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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. 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 (list; graph; refs; listen; history; text; internal format)
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: A238748 A268390 A265693 * A339561 A346014 A006881

Adjacent sequences:  A211481 A211482 A211483 * A211485 A211486 A211487

KEYWORD

nonn,easy

AUTHOR

Douglas Latimer, Apr 12 2012

STATUS

approved

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Last modified September 22 22:38 EDT 2021. Contains 347609 sequences. (Running on oeis4.)