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A245644 Numbers n such that n^3 is an arithmetic number. 2
1, 3, 5, 7, 11, 13, 14, 15, 17, 19, 21, 23, 24, 29, 31, 33, 35, 37, 39, 41, 42, 43, 46, 47, 51, 52, 53, 55, 56, 57, 59, 61, 62, 65, 66, 67, 69, 70, 71, 73, 77, 79, 80, 83, 85, 87, 89, 91, 93, 94, 95, 97, 101, 103, 105, 107, 109, 111, 113, 114, 115, 117, 119, 120, 123, 127, 129, 131, 133, 137, 138, 139 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

A065091 is a subsequence.

LINKS

Reinhard Zumkeller and Jens Kruse Andersen, Table of n, a(n) for n = 1..10000 (first 147 terms from Reinhard Zumkeller)

Wikipedia, Arithmetic number

FORMULA

A245656(a(n)^3) = 1. - Reinhard Zumkeller, Jul 28 2014

MAPLE

isArithPow := proc(n, e)

    local dvs, d ;

    dvs := numtheory[divisors](n^e) ;

    add(d, d=dvs)/nops(dvs) ;

    if type(%, 'integer') then

        true;

    else

        false;

    end if;

end proc:

for n to 300 do

    if isArithPow(n, 3) then

        printf("%d, ", n) ;

    end if;

end do:

MATHEMATICA

Select[Range[120], IntegerQ[DivisorSigma[1, #^3 ]/DivisorSigma[0, #^3 ]] &] (* Michael De Vlieger, Aug 05 2014 after Stefan Steinerberger at A003601 *)

PROG

(Haskell)

a245644 n = a245644_list !! (n-1)

a245644_list = filter ((== 1) . a245656 . (^ 3)) [1..]

-- Reinhard Zumkeller, Jul 28 2014

(Python) from sympy import divisors, divisor_count

[n for n in range(1, 10**3) if not sum(divisors(n**3)) % divisor_count(n**3)] # Chai Wah Wu, Aug 04 2014

CROSSREFS

Cf. A003601, A107924, A107925.

Cf. A245656.

Sequence in context: A285848 A086527 A161554 * A070087 A100933 A320056

Adjacent sequences:  A245641 A245642 A245643 * A245645 A245646 A245647

KEYWORD

nonn

AUTHOR

R. J. Mathar, Jul 28 2014

STATUS

approved

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Last modified November 13 11:24 EST 2018. Contains 317133 sequences. (Running on oeis4.)