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A352876
Numbers k such that the sum of k, the divisors of k, and the numbers < k that are coprime to k, is a perfect power.
0
7, 9, 12, 36, 700, 752, 4081, 18745, 167940, 1095876, 3393680, 5621764, 9950500, 30108516
OFFSET
1,1
COMMENTS
Numbers k such that k + A000203(k) + A023896(k) is in A001597.
EXAMPLE
a(3) = 12 is a term because 12 + A000203(12) + A023896(12) = 12 + 24 + 28 = 64 = 2^6 is a perfect power.
MAPLE
f:= n -> n + n*numtheory:-phi(n)/2 + numtheory:-sigma(n):
g:= proc(n) local t;
igcd(t[2], t=ifactors(n)[2]) > 1
end proc:
select(t -> g(f(t)), [$2..2*10^6]);
MATHEMATICA
ppQ[n_] := GCD @@ FactorInteger[n][[;; , 2]] > 1; Select[Range[10^7], ppQ[# + DivisorSigma[1, #] + #*EulerPhi[#]/2] &] (* Amiram Eldar, Apr 07 2022 *)
CROSSREFS
KEYWORD
nonn,more
AUTHOR
J. M. Bergot and Robert Israel, Apr 06 2022
STATUS
approved