1,1

Is the number of solutions finite? Do solutions to n+kPhi[n]=Sigma[n] exist for all values of k? For k=1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 the number of solutions I know below 1000000 is {1, 7, 2, 2, 1, 5, 3, 3, 0, 1, 1}). Not more for larger k.

If 3*2^n-1 is prime for n>0, then 2^n(3*2^n-1) belongs to the sequence; therefore this sequence is infinite if the sequence of primes of the form 3*2^n-1 (A007505) is infinite. - Matthew Vandermast (ghodges14(AT)comcast.net), Jul 31 2004

3796=4.13.73 and 60610624=64.199.4759 do not belong to the class of numbers mentioned above by Vandermast.

n=44, Phi[n]=20, Sigma[44]=1+2+4+11+22+44=84=44+2.20

ta={{0}}; k=2; Do[g=n; If[Equal[n+k*EulerPhi[n], DivisorSigma[1, n]], ta=Append[ta, n]; Print[n]], {n, 1, 182000000}]; {ta, g}

Cf. A000010, A000203.

A subset of A066679.

Adjacent sequences: A076370 A076371 A076372 this_sequence A076374 A076375 A076376

Sequence in context: A060326 A124852 A097416 this_sequence A097215 A126397 A001488

easy,nonn

Labos E. (labos(AT)ana.sote.hu), Oct 15 2002; more terms Aug 04 2004.