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%I #15 Oct 12 2014 16:58:14
%S 80,880,1920,3140,3880,7305,8080,57755,63405,88880,193920,1188031,
%T 1226221,1794971,7966197,8339125
%N Numbers such that Sum_{i=1..k}{phi(d(i))} = Sum_{i=1..k}{phi(Rev(d(i)))}, where d(i) are the k divisors of n, Rev(d(i)) the reverse of the divisors d(i) and phi(x) the Euler totient function. Numbers with all palindromic divisors are not considered.
%C In general Sum_{i=1..k}{phi(d(i))} = n, where d(i) are the k divisors of n.
%C The numbers that are not considered here belong to A062687, numbers all of whose divisors are palindromic. - _Michel Marcus_, Oct 10 2014
%e Divisors of 3140 are 1, 2, 4, 5, 10, 20, 157, 314, 628, 785, 1570, 3140.
%e Adding the Euler totient function of the reverse of the divisors: phi(1) + phi(2) + phi(4) + phi(5) + phi(01) + phi(02) + phi(751) + phi(413) + phi(826) + phi(587) + phi(0751) + phi(0413) = 3140.
%p with(numtheory); T:=proc(h) local x,y,w; x:=h; y:=0;
%p for w from 1 to ilog10(h)+1 do y:=10*y+(x mod 10); x:=trunc(x/10); od; y; end:
%p P:=proc(q) local a,b,k,n,ok;
%p for n from 1 to q do a:=divisors(n); b:=0; ok:=0;
%p for k from 1 to nops(a) do b:=b+phi(T(a[k]));
%p if a[k]<>T(a[k]) then ok:=1; fi; od;
%p if ok=1 and n=b then print(n); fi; od; end: P(10^9);
%o (PARI) isok(n) = {d = divisors(n); rd = vector(#d, i, subst(Polrev(digits(d[i])), x, 10)); (d != rd) && (n == sum(i=1, #rd, eulerphi(rd[i])));} \\ _Michel Marcus_, Oct 10 2014
%Y Cf. A000010, A196677, A247826.
%K nonn,more,base
%O 1,1
%A _Paolo P. Lava_, Oct 01 2014
%E a(11)-a(16) from _Michel Marcus_, Oct 10 2014
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