cp's OEIS Frontend

A346526 Positive integers k that are the product of two integers greater than 1 and ending with the same digit as k.

%I A346526 #25 Aug 15 2021 13:48:40
%S A346526 25,36,75,96,100,121,125,156,175,200,216,225,231,256,275,276,300,325,
%T A346526 336,341,375,396,400,416,425,441,451,456,475,500,516,525,561,575,576,
%U A346526 600,625,636,651,671,675,676,696,700,725,736,756,775,781,800,816,825,861,875
%N A346526 Positive integers k that are the product of two integers greater than 1 and ending with the same digit as k.
%C A346526 Union of 100*A000027, A053742, A324297 and A346507.
%H A346526 Fung Cheok Yin, <a href="https://oeis.org/wiki/User:FUNG_Cheok_Yin/proof(i)_A346526">Limit of the ratio of a(n) to a(n-1) in A346526</a>, Aug 12 2021.
%F A346526 Lim_{n->infinity} a(n)/a(n-1) = 1.
%e A346526 25 = 5*5, 36 = 6*6, 75 = 5*15, 96 = 6*16, 100 = 10*10, 121 = 11*11, 125 = 5*25, 156 = 6*26, 175 = 5*35, 200 = 10*20, 216 = 6*36, 225 = 15*15, 231 = 11*21, ...
%o A346526 (PARI) isok(k) = my(u=k%10); sumdiv(k, d, (d>1) && (d<k) && ((d%10)==u) && ((k/d % 10) == u)) > 0; \\ _Michel Marcus_, Jul 23 2021
%o A346526 (Lisp)
%o A346526 (setf candidates (list 25)) (setf result nil)
%o A346526 (defun factor (num small-num) (equalp 0 (mod num small-num)))
%o A346526 (defun same-end-digit (num1 num2 num3) (and (equalp (mod num1 10) (mod num2 10)) (equalp (mod num2 10) (mod num3 10))))
%o A346526 (defun good-factor-p (num) (loop for i from 5 to (sqrt num) do ( if (factor num i) ( if (same-end-digit num i (/ num i) ) (return T) ))))
%o A346526 (loop for i from 26 to 9000 do ( if (or (equalp 0 (mod i 10)) (equalp 1 (mod i 10)) (equalp 5 (mod i 10)) (equalp 6 (mod i 10))) (push i candidates)))
%o A346526 (dolist (element candidates) (if (good-factor-p element) (push element result)))
%o A346526 (format t (write-to-string result)) \\ _FUNG Cheok Yin_, Aug 12 2021
%Y A346526 Cf. A000027, A053742, A324297, A346507.
%K A346526 nonn,base
%O A346526 1,1
%A A346526 _Stefano Spezia_, Jul 22 2021