A211485 Numbers n for which the canonical prime factorization contains only an odd number of exponents, all of which are congruent to 1 modulo 3.

1, 2, 3, 5, 7, 11, 13, 16, 17, 19, 23, 29, 30, 31, 37, 41, 42, 43, 47, 53, 59, 61, 66, 67, 70, 71, 73, 78, 79, 81, 83, 89, 97, 101, 102, 103, 105, 107, 109, 110, 113, 114, 127, 128, 130, 131, 137, 138, 139, 149, 151, 154, 157, 163, 165, 167, 170, 173, 174, 179

Offset

1,2

Comments

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

Links

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

Example

3 is included, as its canonical prime factorization 3^1 contains only an odd number of exponents, all of which are congruent to 1 modulo 3.
81 is in the sequence, because its canonical prime factorization is 3^4, and that one exponent, 4, is congruent to 1 modulo 3.

Mathematica

oneQ[n_]:=Module[{f=FactorInteger[n][[All, 2]]}, OddQ[Length[f]]&&Union[ Mod[ f, 3]]=={1}]; Select[Range[200], oneQ] (* Harvey P. Dale, Jul 03 2019 *)

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 != 1, passes=0; break()); if( M[k, 2] % 3 != 1, passes=0));
if( passes == 1 , print1(k, ", "); plnt++) ; if(mxind ==  plnt, break() ))}

Crossrefs

The definition is similar to that for A211484. This sequence includes the prime numbers A000040, and includes A030059.

Sequence in context: A211338 A167175 A026478 * A154893 A084111 A171474

Adjacent sequences: A211482 A211483 A211484 * A211486 A211487 A211488

Keyword

nonn,easy

Author

Douglas Latimer, Apr 12 2012

Status

approved