A245644 Numbers n such that n^3 is an arithmetic number.

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

Offset: 1

Author

R. J. Mathar, Jul 28 2014

Keywords

• nonn

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

Crossrefs

Cf. A003601, A107924, A107925.

Cf. A245656.

Programs

Haskell

a245644 n = a245644_list !! (n-1)
a245644_list = filter ((== 1) . a245656 . (^ 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 *)

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

Formula

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