cp's OEIS Frontend

A241004 Numbers n such that anti-phi(sigma*(n)) = n, where anti-phi is A066452 and sigma* is the sum of anti-divisors of n (A066417).

%I A241004 #13 Mar 01 2016 02:27:38
%S A241004 90,137,162,581,714,773,3735,4557,71028
%N A241004 Numbers n such that anti-phi(sigma*(n)) = n, where anti-phi is A066452 and sigma* is the sum of anti-divisors of n (A066417).
%C A241004 Like A001229 but using anti-phi(n) (A066452) and sigma*(n) (A066417).
%e A241004 90 is in the sequence: Anti-divisors of 90 are 4, 12, 20, 36, 60 and their sum is 132. Anti-phi of 132 is 90.
%p A241004 isA241004 := proc(n)
%p A241004     simplify( n = A066452(A066417(n))) ;
%p A241004 end proc:
%p A241004 for n from 1 do
%p A241004     if isA241004(n) then
%p A241004         printf("%d\n",n) ;
%p A241004     end if;
%p A241004 end do: # _R. J. Mathar_, Aug 07 2014
%o A241004 (PARI) sad(n) = my(k); if(n>1, k=valuation(n, 2); sigma(2*n+1)+sigma(2*n-1)+sigma(n/2^k)*2^(k+1)-6*n-2, 0);
%o A241004 antidiv(n) = {my(v = []); for (k=2, n-1, if (abs((n % k) - k/2) < 1, v = concat(v, k));); v;}
%o A241004 antiphi(n) = {my(vad = antidiv(n)); my(nbad = 0); for (j=1, n-1, isad = 1; for (k=1, #vad, if ((j % vad[k]) == 0, isad = 0; break); ); nbad += isad;); nbad;}
%o A241004 isok(n) = n == antiphi(sad(n)); \\ _Michel Marcus_, Feb 25 2016
%Y A241004 Cf. A001229, A066417, A066452.
%K A241004 nonn,more
%O A241004 1,1
%A A241004 _Paolo P. Lava_, Aug 07 2014
%E A241004 a(9) from _Michel Marcus_, Feb 25 2016