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.

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.

Links

Table of n, a(n) for n=1..14.

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

Cf. A000203, A001597, A023896.

Sequence in context: A121056 A174189 A112529 * A161892 A056528 A055565

Adjacent sequences: A352873 A352874 A352875 * A352877 A352878 A352879

Keyword

nonn,more

Author

J. M. Bergot and Robert Israel, Apr 06 2022

Status

approved