A087485 Odd numbers n such that 2n - sigma(n) = 6.

7, 15, 315, 1155, 815634435

Offset: 1

Author

Farideh Firoozbakht, Oct 23 2003

Keywords

• hard
• more
• nonn

Comments

This is a subsequence of A077374.

Except for the first term, all known terms of this sequence are divisible by 15. Is there a number n > 1 such that gcd(a(n),3)=1 or gcd(a(n),5)=1?

a(6) > 10^13. - Giovanni Resta, Mar 29 2013

Also, a subsequence of A141548. - M. F. Hasler, Apr 12 2015

The terms a(3) through a(5) are of the form a(k)*p*q, but I have proved that there is no other term of this form with k <= 5. - M. F. Hasler, Apr 13 2015

The terms are also of the form a(n) = 2*p(n) + 1, with primes p(n) = 3, 7, 157, 577, 407817217. All but the last one are such that 2*p(n) - 1 = a(n) - 2 is again prime. - M. F. Hasler, Nov 27 2016

Terms a(2..5) satisfy 2*a(n) - nextprime(sigma(a(n))) = (-1)^n, see also A067795. - M. F. Hasler, Feb 14 2017

Examples

			15 is in the sequence because 2*15-sigma(15)=6.
		

Crossrefs

Cf. A077374, A087167, A088011, A088012.

Programs

Mathematica

Do[If[OddQ[n]&&2n-DivisorSigma[1, n]==6, Print[n]], {n, 2*10^9}]

PARI

is(n)=bittest(n,0)&&sigma(n)+6==2*n \\ M. F. Hasler, Apr 12 2015

Formula

a(3) = a(2)*3*7; a(4) = a(2)*7*11 with 7 = precprime(a(2)*2/3), 11=nextprime(a(2)*2/3); a(5) = a(4)*547*1291. - M. F. Hasler, Apr 13 2015