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A225722
Numbers divisible by their last digit cubed, excluding those whose last digit is 1.
3
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
KEYWORD
nonn,base
STATUS
approved