A376119 Abundant numbers that are perfect powers.

36, 100, 144, 196, 216, 324, 400, 576, 784, 900, 1000, 1296, 1600, 1728, 1764, 1936, 2304, 2500, 2704, 2744, 2916, 3136, 3600, 4356, 4624, 4900, 5184, 5776, 5832, 6084, 6400, 7056, 7744, 7776, 8000, 8100, 8464, 9216, 9604, 10000, 10404, 10648, 10816, 11025, 11664, 12100, 12544

Offset

1,1

Comments

Intersection of A001597 and A005101.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

36 is a term being a power (36=6^2) and an abundant number as a multiple of 6.

Maple

N:= 20000: # to get terms <= N
isab:= proc(n) local F, t;
  F:= ifactors(n)[2];
  mul((t[1]^(t[2]+1)-1)/(t[1]-1), t = F) > 2*n
end proc:
S:= select(isab, {seq(seq(x^i, i=2..ilog[x](N)), x=2..isqrt(N))}):
sort(convert(S, list)); # Robert Israel, Sep 12 2024

Mathematica

Select[Range[2*10^4], DivisorSigma[1, #]-2#>0&&GCD@@FactorInteger[#][[All, 2]]>1&]

Prog

(PARI) ok(n)=sigma(n)-2*n>0 && ispower(n)

Crossrefs

Cf. A001597, A005101.

Sequence in context: A072413 A377817 A131605 * A296204 A063734 A069057

Adjacent sequences: A376116 A376117 A376118 * A376120 A376121 A376122

Keyword

nonn

Author

Waldemar Puszkarz, Sep 11 2024

Status

approved