1,1

If p = 3*2^(m-1)-1 is an odd prime then 2^m*p is in the sequence because phi(2^m*p) = 2^(m-1)*(3*2^(m-1)-2), sigma(2^m*p) = (2^(m+1)-1)*(3*2^(m-1)) so phi(2^m*p)+sigma(2^m*p) = 2^(m-1)*(3* 2^(m-1)-2)+(2^(m+1)-1)*(3*2^(m-1)) = 3*2^(2m-2)-2^m+3*2^(2m)-3*2^ (m-1) = 2^(m-1)*(3*2^(m-1)-2+3*2^(m+1)-3) = 2^(m-1)*(3*5*2^(m-1)-5) = 5/2*2^m*(3*2^(m-1)-1) = 5/2*(2^m*p). Except 18 & 5238976 all known terms of the sequence are of the form 2^m*(3*2^(m-1)-1), where (3*2^(m-1)-1) is prime. Next term is greater than 2*10^8.

25161728 is in the sequence because

phi(25161728)+sigma(25161728)=12578816+50325504=5/2*25161728.

Do[If[DivisorSigma[1, n]+EulerPhi[n]==5/2*n, Print[n]], {n, 200000000}]

Cf. A002235.

Sequence in context: A113542 A075865 A066240 this_sequence A001101 A088341 A105145

Adjacent sequences: A115744 A115745 A115746 this_sequence A115748 A115749 A115750

more,nonn

Farideh Firoozbakht (mymontain(AT)yahoo.com), Feb 12 2006