A348962 Exponential harmonic numbers of type 1 (A348961) that are not squarefree.

36, 180, 252, 396, 468, 612, 675, 684, 828, 1044, 1116, 1260, 1332, 1350, 1476, 1548, 1692, 1800, 1908, 1936, 1980, 2124, 2196, 2340, 2412, 2556, 2628, 2700, 2772, 2844, 2988, 3060, 3204, 3276, 3420, 3492, 3636, 3708, 3852, 3924, 4068, 4140, 4284, 4572, 4716

Offset

1,1

Comments

Sándor (2006) proved that all the squarefree numbers are exponential harmonic numbers of type 1.

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

36 = 2^2 * 3^2 is a term since it is not squarefree, A051377(36) = 72, 36 * A049419(36) = 36 * 4 = 144, so A051377(36) | 36 * A049419(36).

Mathematica

f[p_, e_] := p^e * DivisorSigma[0, e] / DivisorSum[e, p^# &]; ehQ[1] = True; ehQ[n_] := IntegerQ[Times @@ f @@@ FactorInteger[n]]; Select[Range[5000], ! SquareFreeQ[#] && ehQ[#] &]

Crossrefs

Intersection of A013929 and A348961.

Cf. A049419, A005117, A051377, A054979, A054980, A348965.

Sequence in context: A211762 A219858 A307958 * A127657 A318100 A335218

Adjacent sequences: A348959 A348960 A348961 * A348963 A348964 A348965

Keyword

nonn

Author

Amiram Eldar, Nov 05 2021

Status

approved