OFFSET
1,1
COMMENTS
Supersequence of A000668 (Mersenne primes) and A067803 (numbers n such that sigma(n) - sigma(n+1) = n).
Corresponding integers k such that sigma(n+1) - sigma(n) = n/k: 2, 1, -4, 1, -4, -2, -13, 1, 1, -1, -1, -1093, -2, 1, ....
a(27) > 10^11. - Donovan Johnson, May 04 2013
a(27) > 10^13. - Giovanni Resta, Aug 01 2013
EXAMPLE
Number 2186 is in sequence because sigma(2187) - sigma(2186) = 3280 - 3282 = -2 which divides 2186.
MATHEMATICA
Select[Range[1000000], DivisorSigma[1, # + 1] - DivisorSigma[1, #] != 0 && IntegerQ[#/(DivisorSigma[1, # + 1] - DivisorSigma[1, #])] &] (* T. D. Noe, May 02 2013 *)
Select[Partition[Table[{n, DivisorSigma[1, n]}, {n, 16*10^5}], 2, 1], Divisible[#[[1, 1]], #[[1, 2]]-#[[2, 2]]]&][[All, 1, 1]]//Quiet (* Harvey P. Dale, Jun 27 2020 *)
Position[MapIndexed[Divisible[#2[[1]], #] &, Subtract @@@ Partition[DivisorSigma[1, Range[10^6]], 2, 1]], True] // Flatten // Quiet (* Eric W. Weisstein, Dec 21 2023 *)
PROG
(PARI) is(n)=my(m=sigma(n+1)-sigma(n)); m && n%m==0 \\ Charles R Greathouse IV, May 02 2013
CROSSREFS
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, May 01 2013
EXTENSIONS
a(15)-a(21) from Charles R Greathouse IV, May 02 2013
a(22)-a(26) from Donovan Johnson, May 04 2013
STATUS
approved