cp's OEIS Frontend

A336192 Numbers of the form ab such that phi(ab) = a*b - 1 where ab is the concatenation of a and b.

%I A336192 #22 Jul 13 2020 13:27:34
%S A336192 1385,1397,15663,19835,37037,238903,719719,1983035,4337785,5946445,
%T A336192 8099989,15276063,64438507,97919791,238639687,325776657,1926629941,
%U A336192 3228792383,4387457627,4652069941,9801019901,44898935609,68135795923,115563539473,129898064149,390084197561
%N A336192 Numbers of the form ab such that phi(ab) = a*b - 1 where ab is the concatenation of a and b.
%C A336192 Is the sequence infinite?
%C A336192 If phi(ab) = a*b - 1 then ab is a composite number.
%e A336192 phi(1385) = 13 * 85 - 1
%e A336192 phi(1397) = 13 * 97 - 1
%e A336192 phi(15663) = 15 * 663 - 1
%e A336192 phi(19835) = 19 * 835 - 1
%e A336192 phi(37037) = 3703 * 7 - 1
%e A336192 phi(238903) = 23 * 8903 - 1
%e A336192 phi(719719) = 719 * 719 - 1
%e A336192 phi(1983035) = 19 * 83035 - 1
%e A336192 phi(4337785) = 4337 * 785 - 1
%e A336192 phi(5946445) = 5 * 946445 - 1
%e A336192 phi(8099989) = 809 * 9989 - 1
%e A336192 phi(15276063) = 1527 * 6063 - 1
%e A336192 phi(64438507) = 6443 * 8507 - 1
%e A336192 phi(97919791) = 9791 * 9791 - 1
%e A336192 phi(238639687) = 23 * 8639687 - 1
%e A336192 phi(325776657) = 32577 * 6657 - 1
%t A336192 seqQ[n_] := Module[{d = IntegerDigits[n]}, MemberQ[Times @@@ Table[FromDigits /@ {Take[d, k], Take[d, -Length[d] + k]}, {k, 1, Length[d] - 1}], EulerPhi[n] + 1]]; Select[Range[10, 10^5], seqQ] (* _Amiram Eldar_, Jul 11 2020 *)
%o A336192 (PARI) isok(m) = {my(tm=eulerphi(m)+1, d=digits(m)); for (i=1, #d-1, if (fromdigits(vector(i, k, d[k]))*fromdigits(vector(#d-i, k, d[i+k])) == tm, return(1)););} \\ _Michel Marcus_, Jul 11 2020
%Y A336192 Cf. A000010, A039649, A336191.
%K A336192 nonn,base,hard
%O A336192 1,1
%A A336192 _M. Farrokhi D. G._, Jul 11 2020
%E A336192 Missing terms 1983035 & 5946445 from _Amiram Eldar_, Jul 11 2020
%E A336192 More terms from _Giovanni Resta_, Jul 13 2020