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

1385, 1397, 15663, 19835, 37037, 238903, 719719, 1983035, 4337785, 5946445, 8099989, 15276063, 64438507, 97919791, 238639687, 325776657, 1926629941, 3228792383, 4387457627, 4652069941, 9801019901, 44898935609, 68135795923, 115563539473, 129898064149, 390084197561

Offset

1,1

Comments

Is the sequence infinite?

If phi(ab) = a*b - 1 then ab is a composite number.

Links

Table of n, a(n) for n=1..26.

Example

phi(1385) = 13 * 85 - 1
phi(1397) = 13 * 97 - 1
phi(15663) = 15 * 663 - 1
phi(19835) = 19 * 835 - 1
phi(37037) = 3703 * 7 - 1
phi(238903) = 23 * 8903 - 1
phi(719719) = 719 * 719 - 1
phi(1983035) = 19 * 83035 - 1
phi(4337785) = 4337 * 785 - 1
phi(5946445) = 5 * 946445 - 1
phi(8099989) = 809 * 9989 - 1
phi(15276063) = 1527 * 6063 - 1
phi(64438507) = 6443 * 8507 - 1
phi(97919791) = 9791 * 9791 - 1
phi(238639687) = 23 * 8639687 - 1
phi(325776657) = 32577 * 6657 - 1

Mathematica

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 *)

Prog

(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

Crossrefs

Cf. A000010, A039649, A336191.

Sequence in context: A156410 A156413 A029819 * A345526 A345780 A302900

Adjacent sequences: A336189 A336190 A336191 * A336193 A336194 A336195

Keyword

nonn,base,hard

Author

M. Farrokhi D. G., Jul 11 2020

Extensions

Missing terms 1983035 & 5946445 from Amiram Eldar, Jul 11 2020

More terms from Giovanni Resta, Jul 13 2020

Status

approved