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

Author

Amiram Eldar, Nov 05 2021

Keywords

• nonn

Comments

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

Examples

			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).
		

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 A348961.

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

Programs

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[#] &]