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A349020
Modified e-perfect numbers (A349019) that are not squarefree.
2
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
József Sándor, On exponentially harmonic numbers, Scientia Magna, Vol. 2, No. 3 (2006), pp. 44-47.
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
KEYWORD
nonn
AUTHOR
Amiram Eldar, Nov 06 2021
STATUS
approved