A349020 Modified e-perfect numbers (A349019) that are not squarefree.

12, 36, 40, 60, 84, 120, 132, 150, 156, 180, 204, 208, 228, 252, 270, 276, 280, 348, 360, 372, 396, 420, 440, 444, 468, 492, 516, 520, 540, 544, 564, 600, 612, 624, 636, 660, 680, 684, 708, 732, 760, 780, 804, 828, 840, 852, 876, 920, 924, 948, 996, 1020, 1040

Offset: 1

Author

Amiram Eldar, Nov 06 2021

Keywords

• nonn

Comments

Since all the squarefree numbers (A005117) are modified e-perfect numbers, these are the nontrivial terms of A349019.

Examples

			12 = 2^2 * 3 is a term since it is not squarefree and A348963(12) = 3 is a divisor of 12.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• József Sándor, On exponentially harmonic numbers, Scientia Magna, Vol. 2, No. 3 (2006), pp. 44-47.
• József Sándor, Selected Chapters of Geomety, Analysis and Number Theory, 2005, pp. 141-145.

Crossrefs

Intersection of A013929 and A349019.

A348965 is a subsequence.

Cf. A005117.

Programs

Mathematica

f[p_, e_] := p^e/DivisorSum[e, p^(e - #) &]; modEPerfQ[1] = True; modEPerfQ[n_] := IntegerQ[Times @@ f @@@ FactorInteger[n]]; Select[Range[1000], ! SquareFreeQ[#] && modEPerfQ[#] &]