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

1,1

Comments

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

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.

Example

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

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[#] &]

Crossrefs

Intersection of A013929 and A349019.

A348965 is a subsequence.

Cf. A005117.

Sequence in context: A205967 A203378 A073543 * A074234 A076515 A371415

Adjacent sequences: A349017 A349018 A349019 * A349021 A349022 A349023

Keyword

nonn

Author

Amiram Eldar, Nov 06 2021

Status

approved