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A371925 Numbers that are the sum of the final digits of the squarefree divisors of some positive integer.

%I A371925 #8 Apr 16 2024 13:59:26
%S A371925 1,2,3,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,36,38,40,42,44,46,48,
%T A371925 52,56,58,60,62,64,68,72,76,80,84,88,92,96,104,108,112,116,120,124,
%U A371925 128,132,136,144,152,156,160,164,168,176,184,188,192,208,212,216,224,232,236,240,244,248,256
%N A371925 Numbers that are the sum of the final digits of the squarefree divisors of some positive integer.
%C A371925 Numbers that occur in A367503.
%H A371925 Robert Israel, <a href="/A371925/b371925.txt">Table of n, a(n) for n = 1..1000</a>
%e A371925 a(10) = 16 is a term because 16 = A367503(39): the squarefree divisors of 39 are 1, 3, 13 and 39, and 1 + 3 + 3 + 9 = 16.
%p A371925 N:= 300: # for terms <= N
%p A371925 g:= proc(pat) local i;
%p A371925    add(pat[i]*i,i=1..9)
%p A371925 end proc:
%p A371925 pats:= {[1,0,0,0,0,0,0,0,0], [1,1,0,0,0,0,0,0,0],[1,0,0,0,1,0,0,0,0],[1,1,0,0,1,0,0,0,0]}:
%p A371925 do newpats:= select(p -> g(p)<=N, map(pat -> 2*pat, pats)) minus pats;
%p A371925   if newpats = {} then break fi; pats:= pats union newpats od:
%p A371925 do newpats:= select(p -> g(p) <=N, map(pat -> pat + [pat[7],pat[4],pat[1],pat[8],pat[5],pat[2],pat[9],pat[6],pat[3]], pats)) minus pats;
%p A371925   if newpats = {} then break fi; pats:= pats union newpats od:
%p A371925 do newpats:= select(p -> g(p)<=N, map(pat -> pat + [pat[3],pat[6],pat[9],pat[2],pat[5],pat[8],pat[1],pat[4],pat[7]], pats)) minus pats;
%p A371925   if newpats = {} then break fi; pats:= pats union newpats od:
%p A371925 do newpats:= select(p -> g(p)<=N, map(pat -> pat + [pat[9],pat[8],pat[7],pat[6],pat[5],pat[4],pat[3],pat[2],pat[1]], pats)) minus pats;
%p A371925   if newpats = {} then break fi; pats:= pats union newpats od:
%p A371925 sort(convert(map(g,pats),list));
%Y A371925 Cf. A367503.
%K A371925 nonn,look
%O A371925 1,2
%A A371925 _Robert Israel_, Apr 12 2024