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

1,2

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

Links

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

Formula

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

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

Example

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.

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]

Crossrefs

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

Sequence in context: A049032 A100354 A352666 * A048008 A048019 A189586

Adjacent sequences: A275355 A275356 A275357 * A275359 A275360 A275361

Keyword

nonn

Author

Robert G. Wilson v, Jul 24 2016

Status

approved