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

Author

Waldemar Puszkarz, Sep 11 2024

Keywords

• nonn

Comments

Intersection of A001597 and A005101.

Examples

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

Links

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

Crossrefs

Cf. A001597, A005101.

Programs

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&]

PARI

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