A159000 Numbers m such that m = s|t = phi(s)*sigma(t) for some numbers s and t, where "|" denotes 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
Examples
3008768 = phi(3008)*sigma(768) so 3008768 is in the sequence.
Links
- Max Alekseyev, Table of n, a(n) for n = 1..51 (first 33 terms from Giovanni Resta)
Programs
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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 *) -
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 */
Extensions
Corrected (a(3), a(4), and a(11) missing), extended past a(12), and edited by Charles R Greathouse IV, Apr 28 2010
Comments