A225722 - OEIS

%I #18 Aug 08 2023 03:22:01

%S 32,64,72,112,125,152,192,216,232,243,272,312,352,375,384,392,432,472,

%T 512,513,552,592,625,632,672,704,712,729,752,783,792,832,872,875,912,

%U 952,992,1024,1032,1053,1072,1112,1125,1152,1192,1232,1272,1296,1312,1323

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

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

%C 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

%H Christian N. K. Anderson, <a href="/A225722/b225722.txt">Table of n, a(n) for n = 1..10000</a>

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

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

%o (R)

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

%Y Subsequence of A225297.

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

%K nonn,base

%O 1,1

%A _Kevin L. Schwartz_ and _Christian N. K. Anderson_, May 13 2013