A336237 -id:A336237 - cp's OEIS frontend

A337523 Numbers of the form ab such that uphi(ab) = a*b where ab is the concatenation of a and b.

18, 26, 68, 87, 154, 165, 209, 572, 846, 1434, 4840, 5476, 5828, 5936, 6499, 6572, 7772, 8540, 8727, 10088, 10864, 11772, 12867, 15088, 20099, 20584, 20881, 21672, 22440, 27348, 29748, 29920, 30576, 32390, 35640, 36580, 37200, 37449, 38430, 39600, 40548, 42984

Offset: 1

Marius A. Burtea, Aug 30 2020

			For k = 18, uphi(18) = 8 = 1 * 8.
For k = 68, uphi(68) = 48 = 6 * 8.
For k = 87, uphi(87) = 56 = 8 * 7.
For k = 154, uphi(154) = 60 = 15 * 4.

Cf. A047994 (uphi), A336237.

uphi:=func; [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)}];

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 *)

cp's OEIS Frontend

A337523 Numbers of the form ab such that uphi(ab) = a*b where ab is the concatenation of a and b.

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