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A340588 Squares of perfect powers. 1
1, 16, 64, 81, 256, 625, 729, 1024, 1296, 2401, 4096, 6561, 10000, 14641, 15625, 16384, 20736, 28561, 38416, 46656, 50625, 59049, 65536, 83521, 104976, 117649, 130321, 160000, 194481, 234256, 262144, 279841, 331776, 390625, 456976, 531441, 614656, 707281, 810000, 923521, 1000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..41.

FORMULA

a(n) = A001597(n)^2.

a(n+1) = A062965(n) + 1. - Hugo Pfoertner, Sep 29 2020

Sum_{k>1} 1/(a(k) - 1) = 7/4 - Pi^2/6 = 7/4 - zeta(2).

Sum_{k>1} 1/a(k) = Sum_{k>=2} mu(k)*(1-zeta(2*k)).

MATHEMATICA

Join[{1}, (Select[Range[2000], GCD @@ FactorInteger[#][[All, 2]] > 1 &])^2]

CROSSREFS

Cf. A000290, A001597, A062965, A072102, A117453, A131605.

Sequence in context: A233330 A322449 A117453 * A305242 A039370 A324880

Adjacent sequences:  A340585 A340586 A340587 * A340589 A340590 A340591

KEYWORD

nonn

AUTHOR

Terry D. Grant, Sep 21 2020

STATUS

approved

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Last modified November 28 18:39 EST 2021. Contains 349415 sequences. (Running on oeis4.)