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 A336192 Numbers of the form ab such that phi(ab) = a*b - 1 where ab is the concatenation of a and b. 2
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified September 27 15:26 EDT 2023. Contains 365711 sequences. (Running on oeis4.)