A115069 - OEIS

A115069

a(n) = 3^b(n), where b(n) is #{primes p=1 mod 3 dividing n}.

1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 3, 3, 1, 1, 1, 1, 3, 1, 3, 1, 1, 1, 1, 3, 1, 3, 1, 1, 3, 1, 1, 1, 3, 1, 3, 3, 3, 1, 1, 3, 3, 1, 1, 1, 1, 1, 3, 1, 1, 3, 1, 1, 1, 3, 3, 1, 1, 1, 3, 3, 3, 1, 3, 1, 3, 1, 1, 3, 1, 1, 3, 3, 1, 3, 3, 3, 3, 1, 1, 1, 1, 3, 1, 3, 1, 1, 1, 1, 9, 1, 3, 1, 3, 1, 3, 3, 1

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OFFSET

1,7

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

Steven Finch and Pascal Sebah, Squares and Cubes Modulo n, arXiv:math/0604465 [math.NT], 2006-2016.

FORMULA

a(n) = 3^A005088(n). - R. J. Mathar, May 19 2020

MAPLE

a:= n-> 3^add(`if`(irem(i[1], 3)=1, 1, 0), i=ifactors(n)[2](n)):

seq(a(n), n=1..100); # Alois P. Heinz, Feb 17 2019

MATHEMATICA

b[n_] := Count[FactorInteger[n][[All, 1]], p_ /; Mod[p, 3] == 1];

a[1] = 1; a[n_] := 3^b[n];

Table[a[n], {n, 1, 99}] (* Jean-François Alcover, Feb 17 2019 *)

CROSSREFS

Cf. A005088, A060839.

Sequence in context: A317624 A328575 A106478 * A046556 A046535 A324198

Adjacent sequences: A115066 A115067 A115068 * A115070 A115071 A115072

KEYWORD

nonn

AUTHOR

Steven Finch, Mar 01 2006

EXTENSIONS

a(1)=1 prepended by Alois P. Heinz, Feb 17 2019

STATUS

approved