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 A087485 Odd numbers n such that 2n - sigma(n) = 6. 8
 7, 15, 315, 1155, 815634435 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 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 LINKS 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 EXAMPLE 15 is in the sequence because 2*15-sigma(15)=6. MATHEMATICA Do[If[OddQ[n]&&2n-DivisorSigma[1, n]==6, Print[n]], {n, 2*10^9}] PROG (PARI) is(n)=bittest(n, 0)&&sigma(n)+6==2*n \\ M. F. Hasler, Apr 12 2015 CROSSREFS Cf. A077374, A087167, A088011, A088012. Sequence in context: A041096 A248275 A007541 * A156377 A069526 A061039 Adjacent sequences:  A087482 A087483 A087484 * A087486 A087487 A087488 KEYWORD hard,more,nonn AUTHOR Farideh Firoozbakht, Oct 23 2003 STATUS approved

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Last modified June 15 22:06 EDT 2021. Contains 345053 sequences. (Running on oeis4.)