A275358 The difference between A089580(n) and A089579(n).

0, 4, 10, 20, 41, 65, 114, 185, 297, 487, 809, 1339, 2253, 3824, 6544, 11297, 19620, 34216, 59926, 105258, 185356, 327039, 577906, 1022466, 1810789, 3209398, 5691825, 10099475, 17927609, 31833805, 56541947, 100449345, 178484340, 317187186, 563744378, 1002052726

Offset: 1

Author

Robert G. Wilson v, Jul 24 2016

Keywords

• nonn

Comments

Submitted on the request of Omar E. Pol 17 July 2016. (A089579).

a(n) is the sum of A175066(m)-1 over such m that A117453(m)<10^n. - Andrey Zabolotskiy, Aug 17 2016

Examples

			a(2) = A089580(2)-A089579(2) = 4 because of the three terms: 16 = 2^4 = 4^2, 64 = 2^6 = 4^3 = 8^2 and 81 = 3^4 = 9^2; one for 16, two for 64 and one for 81 making a total of 4.
		

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A011007, A011557, A070428, A089579, A089580.

Programs

Mathematica

f[n_] := Block[{lim = 10^n -1}, Sum[ (Floor[ lim^(1/k)] - 1)(1 + MoebiusMu[k]), {k, 2, Floor[ Log[2, lim]]}]]; Array[f, 36]

Formula

a(n) = A089580(n) - A089579(n).

Limit_{n->oo} a(n+1)/a(n) = 1.778279... (A011007). - Altug Alkan, Aug 22 2016