A337523 - OEIS

%I #12 Sep 08 2022 08:46:25

%S 18,26,68,87,154,165,209,572,846,1434,4840,5476,5828,5936,6499,6572,

%T 7772,8540,8727,10088,10864,11772,12867,15088,20099,20584,20881,21672,

%U 22440,27348,29748,29920,30576,32390,35640,36580,37200,37449,38430,39600,40548,42984

%N Numbers of the form ab such that uphi(ab) = a*b where ab is the concatenation of a and b.

%e For k = 18, uphi(18) = 8 = 1 * 8.

%e For k = 68, uphi(68) = 48 = 6 * 8.

%e For k = 87, uphi(87) = 56 = 8 * 7.

%e For k = 154, uphi(154) = 60 = 15 * 4.

%t f[p_, e_] := p^e - 1; uphi[1] = 1; uphi[n_] := Times @@ f @@@ FactorInteger[n]; seqQ[n_] := Module[{d = IntegerDigits[n]}, MemberQ[Times @@@ Table[FromDigits /@ {Take[d, k], Take[d, -Length[d] + k]}, {k, 1, Length[d] - 1}], uphi[n]]]; Select[Range[10, 43000], seqQ] (* _Amiram Eldar_, Aug 30 2020 *)

%o (Magma) uphi:=func<n|n eq 1 select 1 else &*[d[1]^d[2]-1: d in Factorization(n)]>; [k:k in [10..43000]| exists(c){i:i in [1..#Intseq(k)-1]| (k mod 10^i)*(k div 10^i) ne 0 and (k mod 10^i)*(k div 10^i) eq uphi(k)}];

%Y Cf. A047994 (uphi), A336237.

%K nonn,base

%O 1,1

%A _Marius A. Burtea_, Aug 30 2020