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

1,1

Links

Table of n, a(n) for n=1..42.

Example

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.

Mathematica

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 *)

Prog

(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)}];

Crossrefs

Cf. A047994 (uphi), A336237.

Sequence in context: A212052 A093018 A284493 * A167336 A328687 A003634

Adjacent sequences: A337520 A337521 A337522 * A337524 A337525 A337526

Keyword

nonn,base

Author

Marius A. Burtea, Aug 30 2020

Status

approved