A112728
Numbers k such that geometric mean of phi(k), k and sigma(k) is an integer.
Original entry on oeis.org
1, 37044, 1222452, 193637687880
Offset: 1
(phi(1222452)*1222452*sigma(1222452))^(1/3)=1164240 is an integer, so 1222452 is a term of the sequence.
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Do[If[IntegerQ[(n*DivisorSigma[1, n] EulerPhi[n])^(1/3)], Print[n]], {n, 600000000}]
A306724
Least number k > 1 such that A062354(k) is an n-th power, where A062354 is the product of sigma (A000203) and phi (A000010).
Original entry on oeis.org
2, 14, 3, 170, 3570, 592922491, 17194752239, 498892319051, 14467877252479, 421652049419104, 12227909433154016, 377536703748630244, 926952707565364023467, 1485824943636552705389704010031591742370238670767627108613, 18031470774665264926975299618474551942701594055200456829621877, 219559123426400144842876467461078524942414020727022446946702813568
Offset: 1
A062354(14) = 12^2;
A062354(3) = 2^3;
A062354(170) = 12^4;
A062354(3570) = 24^5;
A062354(592922491) = 840^6;
A062354(17194752239) = 840^7.
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a[n_] := Module[{k=2}, While[!IntegerQ[Surd[DivisorSigma[1, k]*EulerPhi[k], n]], k++]; k]; Array[a, 1, 5]
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a(n) = {my(k=2); while (!ispower(sigma(k)*eulerphi(k), n), k++); k;} \\ Michel Marcus, Mar 06 2019
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