1,1

n is necessarily composite.

From the Math. Rev.: if both q=7*2^{r-2}+2^s-1 and p=49*2^{2r-s-4}+7*2^{r-2}-5*2^{r-s-2}-1 are prime for 1 <= s < r-2, then n=2^r*3*p*q is a solution to the equation phi(n)+sigma(n)=3n . [R. K. Guy]

If 7*2^n-1 is prime then m = 2^(n+2)*3*(7*2^n-1) is in the sequence. Because phi(m) = 2^(n+2)*(7*2^n-2); sigma(m) = 7*2^(n+2)*(2^(n+3)-1) so phi(m)+sigma(m) = 2^(n+2)*((7*2^n-2)+(7*2^(n+3)-7)) = 2^(n+2)*(63*2^n-9) = 3*(2^(n+2)*3*(7*2^n-1)) = 3*m. Hence A112729 = 2^(A001771+2)*3*(7*2^A001771-1) is a subsequence of this sequence. - Farideh Firoozbakht (mymontain(AT)yahoo.com), Dec 01 2005

If both numbers p=7*2^n+2^k-1 & q=49*2^(2n-k)+2^(n-k)*(7*2^k-5)-1 are prime and m=2^(n+2)*3*p*q then phi(m)+sigma(m)=3*m. Namely m is in the sequence. - Farideh Firoozbakht (mymontain(AT)yahoo.com), Jan 11 2007

R. K. Guy, Divisors and desires, Amer. Math. Monthly, 104 (1997), 359-360.

ZHANG, Ming Zhi, A note on the equation phi(n)+sigma(n)=3n, Sichuan Daxue Xuebao 37 (2000), no. 1, 39-40; MR1755990 (2001a:11009).

Cf. A001771, A112729, A011254, A011774, A015704.

Sequence in context: A139638 A112542 A011774 this_sequence A043360 A022044 A156403

Adjacent sequences: A011248 A011249 A011250 this_sequence A011252 A011253 A011254

nonn,nice

N. J. A. Sloane (njas(AT)research.att.com).

More terms from Jud McCranie (j.mccranie(AT)comcast.net)