cp's OEIS Frontend

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

%I A211484 #16 Jul 28 2025 08:16:14
%S A211484 1,6,10,14,15,21,22,26,33,34,35,38,39,46,48,51,55,57,58,62,65,69,74,
%T A211484 77,80,82,85,86,87,91,93,94,95,106,111,112,115,118,119,122,123,129,
%U A211484 133,134,141,142,143,145,146,155,158,159,161,162,166,176,177,178,183
%N A211484 Numbers for which the canonical prime factorization contains only an even number of exponents, all of which are congruent to 1 modulo 3.
%C A211484 By convention 1 is included as the first term, in order to simplify the statement of certain results involving this sequence.
%H A211484 Douglas Latimer, <a href="/A211484/b211484.txt">Table of n, a(n) for n = 1..1000</a>
%e A211484 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.
%t A211484 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 *)
%o A211484 (PARI) {plnt=1; k=1; print1(k, ", "); plnt++;
%o A211484 mxind=76 ; mxind++ ; for(k=2, 10^6,
%o A211484 M=factor(k);passes=1;
%o A211484 sz = matsize(M)[1];
%o A211484 for(k=1,sz, if(sz%2 != 0, passes=0;break()); if( M[k,2] % 3 != 1, passes=0));
%o A211484 if( passes == 1 , print1(k, ", "); plnt++) ; if(mxind ==  plnt, break() ))}
%o A211484 (PARI) is(n,f=factor(n))=omega(f)%2==0 && factorback(f[,2]%3)==1 \\ _Charles R Greathouse IV_, Sep 07 2017
%Y A211484 This sequence includes A030229 and hence A006881. The definition is similar to that for A211485.
%K A211484 nonn,easy
%O A211484 1,2
%A A211484 _Douglas Latimer_, Apr 12 2012