A112729 Numbers of the form 2^(k+2)*3*(7*2^k-1) where 7*2^k-1 is prime.

312, 85632, 22013952, 1443107438592, 369435881766912, 24211351590301335552, 103986963299971520879061368832

Offset: 1

Author

Farideh Firoozbakht, Dec 01 2005

Keywords

• easy
• nonn

Comments

This sequence is a subsequence of A011251 and A011774, namely if m is in the sequence then phi(m)+sigma(m)=3*m (see Comments line of A011251).

Number of digits of all the 20 known terms of this sequence are respectively 3, 5, 8, 13, 15, 20, 30, 109, 11069, 13566, 14787, 15722, 20988, 25263, 40594, 42272, 101802, 104453, 107155 and 219110.

Examples

			103986963299971520879061368832 is in the sequence because 103986963299971520879061368832=2^(45+2)*3*(7*2^45-1) and 7*2^45-1 is prime.
		

Crossrefs

Cf. A001771. A011251, A011774.

Programs

Mathematica

Do[If[PrimeQ[7*2^n-1], Print[3*2^(n+2)*(7*2^n-1)]], {n, 177}]