login
A376119
Abundant numbers that are perfect powers.
0
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.
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
Sequence in context: A250812 A072413 A131605 * A296204 A063734 A069057
KEYWORD
nonn
AUTHOR
Waldemar Puszkarz, Sep 11 2024
STATUS
approved