A159000 Numbers n such that there exist two numbers a and b where n=a.b=phi(a)*sigma(b)("." means concatenation).

3360, 19440, 35712, 55800, 120960, 395808, 451584, 548640, 628992, 695520, 763344, 3008768, 3749760, 5602320, 17557344, 46902240, 55031040, 119627904, 162496048, 193933440, 243855360, 249793920, 374473800, 377677440, 548402400

Offset

1,1

Comments

A159001(n) give the first part a of a(n).

Links

Giovanni Resta, Table of n, a(n) for n = 1..33

Example

3008768 = phi(3008)*sigma(768) so 3008768 is in the sequence.

Mathematica

ntnQ[n_]:=MemberQ[(EulerPhi[#[[1]]]DivisorSigma[1, #[[2]]])==n&/@ Table[FromDigits/@TakeDrop[IntegerDigits[n], i], {i, IntegerLength[ n]-1}], True]; Select[Range[55*10^7], ntnQ] (* The program uses the TakeDrop function from Mathematica version 10 *) (* The program takes a long time to run *) (* Harvey P. Dale, Jan 01 2016 *)

Prog

(PARI) isA159000(n)={my(m); for(i=1, #Str(n)-1, m=n%10^i; if(m, m=divrem(n, sigma(m)); if(m[2]==0&eulerphi(n\10^i)==m[1], return(i)))); 0} /* Charles R Greathouse IV, Apr 28 2010 */

Crossrefs

Cf. A159001, A253824, A260144.

Sequence in context: A104938 A179704 A222154 * A032773 A323965 A223295

Adjacent sequences: A158997 A158998 A158999 * A159001 A159002 A159003

Keyword

nonn,base

Author

Farideh Firoozbakht, Jun 04 2009

Extensions

Corrected (a(3), a(4), and a(11) missing), extended past a(12), and edited by Charles R Greathouse IV, Apr 28 2010

Status

approved