cp's OEIS Frontend

A336191 Numbers k of the form k = ab (the decimal concatenation of a and b) such that phi(ab) = a*b + 1.

%I A336191 #32 Jul 13 2020 21:38:39
%S A336191 57,195,319,5595,11709,77097,114765,1313667,1348559,4752465,10219099,
%T A336191 11031119,185573199,2918945715,3165616929,12233666703,16996664613,
%U A336191 18052811909,20650199699,38081370319,58943659521,195823876095,236323024041,242687655369,342764528277,677924155713
%N A336191 Numbers k of the form k = ab (the decimal concatenation of a and b) such that phi(ab) = a*b + 1.
%C A336191 Is the sequence infinite?
%e A336191 phi(57) = 5 * 7 + 1
%e A336191 phi(195) = 1 * 95 + 1 = 19 * 5 + 1
%e A336191 phi(319) = 31 * 9 + 1
%e A336191 phi(5595) = 5 * 595 + 1
%e A336191 phi(11709) = 11 * 709 + 1
%e A336191 phi(77097) = 7 * 7097 + 1
%e A336191 phi(114765) = 11 * 4765 + 1
%e A336191 phi(1313667) = 1313 * 667 + 1
%e A336191 phi(1348559) = 134855 * 9 + 1
%e A336191 phi(4752465) = 47 * 52465 + 1
%e A336191 phi(10219099) = 1021 * 9099 + 1
%e A336191 phi(11031119) = 1103111 * 9 + 1
%e A336191 phi(185573199) = 185 * 573199 + 1
%t A336191 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 A336191 (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 A336191 Cf. A000010, A109606, A336192.
%K A336191 nonn,base,hard
%O A336191 1,1
%A A336191 _M. Farrokhi D. G._, Jul 11 2020
%E A336191 Missing terms 1348559 & 4752465, and a(12) from _Amiram Eldar_, Jul 11 2020
%E A336191 More terms from _Giovanni Resta_, Jul 13 2020