A246907 Numbers n such that sigma(n + sigma(n)) = 3n.

1, 2, 4, 8, 16, 64, 128, 2048, 262144, 17179869184, 274877906944, 8796093022208, 36028797018963968

Offset: 1

Author

Jaroslav Krizek, Sep 07 2014

Keywords

• nonn
• more

Comments

Conjecture: for n >= 2; numbers n of the form 2^k such that 3*(2^k) - 1 is prime. The next terms: 18446744073709551616, 75557863725914323419136, 19807040628566084398385987584, … Sequence of numbers k: 1, 2, 3, 4, 6, 7, 11, 18, 34, 38, 43, 55, 64, 76, … Subsequence of A087370 (numbers n such that 3n - 1 is a prime).

a(14) > 5*10^17. - Hiroaki Yamanouchi, Sep 11 2015

Examples

			Number 16 is in sequence because sigma(16 + sigma(16)) = sigma(16 + 31) = sigma(47) = 48 = 3 * 16.
		

Crossrefs

Cf. A000203, A087370, A246906.

Programs

Magma

[n:n in[1..10000000] | SumOfDivisors(n+SumOfDivisors(n))eq 3*n]

Mathematica

Select[Range[300000], DivisorSigma[1, # + DivisorSigma[1, #]] == 3 # &] (* Harvey P. Dale, Jul 19 2015 *)

PARI

for(n=1,10^7,if(sigma(n+sigma(n))==3*n,print1(n,", "))) \\ Derek Orr, Sep 07 2014

Extensions

a(10)-a(13) from Hiroaki Yamanouchi, Sep 11 2015