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%I #19 Jan 01 2016 11:31:09
%S 3360,19440,35712,55800,120960,395808,451584,548640,628992,695520,
%T 763344,3008768,3749760,5602320,17557344,46902240,55031040,119627904,
%U 162496048,193933440,243855360,249793920,374473800,377677440,548402400
%N Numbers n such that there exist two numbers a and b where n=a.b=phi(a)*sigma(b)("." means concatenation).
%C A159001(n) give the first part a of a(n).
%H Giovanni Resta, <a href="/A159000/b159000.txt">Table of n, a(n) for n = 1..33</a>
%e 3008768 = phi(3008)*sigma(768) so 3008768 is in the sequence.
%t 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 *)
%o (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 */
%Y Cf. A159001, A253824, A260144.
%K nonn,base
%O 1,1
%A _Farideh Firoozbakht_, Jun 04 2009
%E Corrected (a(3), a(4), and a(11) missing), extended past a(12), and edited by _Charles R Greathouse IV_, Apr 28 2010
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