A225722 Numbers divisible by their last digit cubed, excluding those whose last digit is 1.

32, 64, 72, 112, 125, 152, 192, 216, 232, 243, 272, 312, 352, 375, 384, 392, 432, 472, 512, 513, 552, 592, 625, 632, 672, 704, 712, 729, 752, 783, 792, 832, 872, 875, 912, 952, 992, 1024, 1032, 1053, 1072, 1112, 1125, 1152, 1192, 1232, 1272, 1296, 1312, 1323

Offset: 1

Author

Kevin L. Schwartz and Christian N. K. Anderson, May 13 2013

Keywords

• nonn
• base

Comments

a(n) ~ n. For 69 < n < 10000, the formula 26.61*n - 2.76 provides an estimate of a(n) to within 1%.

The asymptotic density of this sequence is 601296607/16003008000 = 0.037573... . Therefore, contrary to the above comment, a(n) ~ c*n where c = 16003008000/601296607 = 26.614166... . - Amiram Eldar, Aug 08 2023

Examples

			a(5) = 125 is an example because its last digit is 5, and 5^3 = 125, and 125 is divisible by 125.
		

Links

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

Crossrefs

Subsequence of A225297.

Cf. A221651, A225296, A132359, A034709, A034837, A005349, A007602, A034838.

Programs

Mathematica

dldcQ[n_]:=Module[{ld=Last[IntegerDigits[n]]},ld>1&&Divisible[n,ld^3]]; Select[Range[1500],dldcQ] (* Harvey P. Dale, Aug 15 2014 *)

R

which(sapply(1:1000,function(x) x%%10>1 & (v=x/(x%%10)^3)==as.integer(v) ))