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

1,1

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

Links

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

Example

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

Mathematica

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

Prog

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

Crossrefs

Subsequence of A225297.

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

Sequence in context: A206371 A255561 A116318 * A195330 A122616 A174312

Adjacent sequences: A225719 A225720 A225721 * A225723 A225724 A225725

Keyword

nonn,base

Author

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

Status

approved