A225297 Numbers divisible by their last digit cubed.

1, 11, 21, 31, 32, 41, 51, 61, 64, 71, 72, 81, 91, 101, 111, 112, 121, 125, 131, 141, 151, 152, 161, 171, 181, 191, 192, 201, 211, 216, 221, 231, 232, 241, 243, 251, 261, 271, 272, 281, 291, 301, 311, 312, 321, 331, 341, 351, 352, 361, 371, 375, 381, 384, 391

Offset: 1

Author

Kevin L. Schwartz and Christian N. K. Anderson, May 04 2013

Keywords

• nonn
• base

Comments

Numbers k such that (k mod 10)^3 | k.

All numbers ending in 1 are trivially included in this sequence.

The sequence is { 1+10k, 32 + 40k, 243 + 270k, 64 + 320k, 125 + 250k, 216 + 1080k, 3087 + 3430k, 2048 + 2560k, 729 + 7290k ; k = 0,1,2,...}. - M. F. Hasler, Jan 31 2016

The asymptotic density of this sequence is 2201597407/16003008000 = 0.137573... . - Amiram Eldar, Aug 08 2023

Examples

			a(16) = 112 is divisible by 2^3.
		

Links

• Christian N. K. Anderson, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A132359, A034709, A034837, A005349, A007602, A034838.

Programs

Mathematica

Select[Range[400], (m = Mod[#, 10]) > 0 && Divisible[#, m^3] &] (* Amiram Eldar, Aug 08 2023 *)

PARI

is(n)=n%10&&n%(n%10)^3==0 \\ M. F. Hasler, Jan 31 2016

R

x=0; y=rep(0,100); len=0; isint<-function(x) x==as.integer(x); while(len<100) if((x=x+1)%%10>0) if(isint(x/(x%%10)^3)) y[(len=len+1)]=x