A345019 Numbers whose last digit is refactorable.

1, 2, 8, 9, 11, 12, 18, 19, 21, 22, 28, 29, 31, 32, 38, 39, 41, 42, 48, 49, 51, 52, 58, 59, 61, 62, 68, 69, 71, 72, 78, 79, 81, 82, 88, 89, 91, 92, 98, 99, 101, 102, 108, 109, 111, 112, 118, 119, 121, 122, 128, 129, 131, 132, 138, 139, 141, 142, 148, 149, 151, 152, 158, 159

Offset

1,2

Comments

Numbers ending in 1, 2, 8 or 9.

Links

Table of n, a(n) for n=1..64.

Wikipedia, Refactorable number.

Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).

Formula

a(n) = 10*floor((n-1)/4)+(10+(-1)^n+7*cos(n*Pi/2)-7*sin(n*Pi/2))/2.

Sum_{n>=1} (-1)^(n+1)/a(n) = sqrt((1+1/sqrt(5))/2)*Pi/5. - Amiram Eldar, Apr 15 2023

G.f.: x*( 1+x+6*x^2+x^3+x^4 ) / ( (1+x)*(1+x^2)*(x-1)^2 ). - R. J. Mathar, Mar 25 2024

Example

158 is in the sequence since 8 is a refactorable number.

Mathematica

Table[10*Floor[(n - 1)/4] + (10 + (-1)^n + 7*Cos[n*Pi/2] - 7*Sin[n*Pi/2]) / 2, {n, 100}]

Crossrefs

Cf. A033950 (refactorable numbers).

Sequence in context: A282636 A019511 A103190 * A116039 A030334 A338807

Adjacent sequences: A345016 A345017 A345018 * A345020 A345021 A345022

Keyword

nonn,easy,base

Author

Wesley Ivan Hurt, Jun 05 2021

Status

approved