%I #19 Dec 19 2024 10:07:32
%S 240,5625,40625,1640625,4140625,39495680,47265625,56640625,3574214656,
%T 66247700480,115760971776,233469644963840,1298980712890625,
%U 6544914573295616,6233428515519201280
%N Composite integers m such that the sum of the integers x <= m not coprime to m ends with digits of m.
%C In other words, number m/2*(m+1-phi(m)) ends with digits of m.
%C Primes form trivial solutions. In fact, for a prime p, we have that phi(p) = p-1 and p/2*(p+1-(p-1)) = p.
%C a(16) > 10^20. - _Max Alekseyev_, Dec 19 2024
%e For m = 240, we have phi(240) = 64 and 240/2*(241-64) = 21240 ends with 240.
%p with(numtheory); P:=proc(q) local a,b,n;
%p for n from 1 to q do a:=n; b:=0; while a>0 do b:=b+1; a:=trunc(a/10); od;
%p if n=(((n/2*(n+1-phi(n))) mod 10^b) then print(n); fi; od; end: P(10^9);
%Y Cf. A000010, A239244.
%K nonn,more,base
%O 1,1
%A _Paolo P. Lava_, Mar 13 2014
%E a(6)-a(11) from _Giovanni Resta_, Mar 14 2014
%E Edited and a(12)-a(15) added by _Max Alekseyev_, Dec 15 2024