

A071404


Which nonsquarefree number is a square number? a(n)th nonsquarefree number equals n^2, the nth square.


1



1, 3, 5, 9, 13, 18, 25, 31, 39, 46, 55, 66, 76, 86, 99, 112, 125, 142, 157, 172, 187, 206, 225, 244, 264, 285, 307, 328, 353, 377, 400, 429, 453, 480, 507, 534, 562, 593, 623, 656, 691, 725, 762, 795, 831, 867, 904, 941, 977, 1019, 1059, 1101, 1145, 1185, 1226
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OFFSET

2,2


LINKS

Table of n, a(n) for n=2..56.


FORMULA

A013929(a(n)) = A000290(n) = n^2.
a(n) = kn^2 + O(n), where k = 1  6/Pi^2.  Charles R Greathouse IV, Sep 13 2013


EXAMPLE

The first, 3rd, 5th, 9th, 13th nonsquarefree numbers are 4,9,16,25,36.


PROG

(PARI) lista(nn) = {sqfs = select(n>(1issquarefree(n)), vector(nn, i, i)); for (i = 1, #sqfs, if (issquare(sqfs[i]), print1(i, ", ")); ); } \\ Michel Marcus, Sep 12 2013
(PARI) a(n)=n^2sum(k=1, n, n^2\k^2*moebius(k)) \\ Charles R Greathouse IV, Sep 13 2013


CROSSREFS

Cf. A005117, A013929, A000040, A000290, A071403.
Sequence in context: A024403 A129230 A203567 * A074133 A215909 A078735
Adjacent sequences: A071401 A071402 A071403 * A071405 A071406 A071407


KEYWORD

nonn


AUTHOR

Labos Elemer, May 24 2002


EXTENSIONS

Offset changed by Charles R Greathouse IV, Sep 13 2013


STATUS

approved



