A266227 a(n) = floor(Sum_{d|n} 1/sigma(d)).

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1

Offset: 1

Author

Jaroslav Krizek, Dec 24 2015

Keywords

• nonn

Comments

Sequence of numbers n such that floor(Sum_{d|n} 1/sigma(d)) = k for k = 1, 2, 3:

k = 1: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, ... (A265711);

k = 2: 60, 72, 84, 90, 120, 144, 168, 180, 210, 216, 240, 252, ... (A265712);

k = 3: 110880, 166320, 221760, 277200, 327600, 332640, 360360, ... (A265713).

Examples

			For n = 6; a(6) = floor(Sum_{d|6} 1/sigma(d)) = floor(1/1 + 1/3 + 1/4 + 1/12) = floor(5/3) = 1.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384

Crossrefs

Cf. A069934, A000203, A265708, A265709, A265710, A265711, A265712, A265713, A265714, A266228.

Programs

Magma

[Floor(&+[1/SumOfDivisors(d): d in Divisors(n)]): n in [1..100]]

Mathematica

A266227[n_] := Floor[DivisorSum[n, 1/DivisorSigma[1, #]&]];
Array[A266227, 100] (* Paolo Xausa, Feb 06 2024 *)

PARI

A266227(n) = { my(s=sumdiv(n,d,1/sigma(d))); (numerator(s) \ denominator(s)); }; \\ Antti Karttunen, Nov 19 2017

Formula

a(n) = floor(Sum_{d|n} 1/A000203(d)).

a(n) = floor(A265708(n) / A069934(n)) = floor(A265709(n) / A265710(n)).