OFFSET
1,2
COMMENTS
All numbers 9m, m > 0, belong to this sequence.
All numbers 6m, m > 0, belong to this sequence. - Christian Schulz, Oct 30 2013
All numbers 280m, m > 0, belong to this sequence. Only 6, 9, 280, and their multiples have this property. - Charles R Greathouse IV, Dec 26 2013
Conjecture: All k-multiply perfect numbers belong to this sequence. - Ivan N. Ianakiev, May 10 2016
The asymptotic density of this sequence is 1321/2520 = 0.524206... (see A074947 and A074949 for the values in other base representations). - Amiram Eldar, Nov 24 2022
The even perfect numbers are a subsequence. It is an open question whether the odd perfect numbers are a subsequence; this would involve ruling out 148 residue classes mod 2520 as OPNs. - Charles R Greathouse IV, Jan 03 2023
LINKS
Ray Chandler, Table of n, a(n) for n = 1..4196 (first 1000 terms from Harry J. Smith)
FORMULA
a(n) = a(n-1321) + 2520. - Charles R Greathouse IV, Dec 26 2013
2520n/1321 - 10 < a(n) <= 2520n/1321. (In fact, if you exclude n = 10 mod 1321, you can replace 10 with 9.) - Charles R Greathouse IV, Jan 03 2023
a(n) = a(n-1) + a(n-1321) - a(n-1322). - Charles R Greathouse IV, Apr 20 2023
EXAMPLE
48: 4 + 8 = 12 -> 1 + 2 = 3. 48 = 3 * 16 therefore 48 = a(28).
MAPLE
A064807 := proc(n) option remember: local k: if(n=1)then return 1:fi: for k from procname(n-1)+1 do if(k mod (((k-1) mod 9) + 1) = 0)then return k: fi: od: end: seq(A064807(n), n=1..100); # Nathaniel Johnston, May 05 2011
MATHEMATICA
Select[Range[125], Divisible[#, Mod[# - 1, 9] + 1] &] (* Alonso del Arte, Nov 01 2013 *)
PROG
(PARI) n=0; for (m=1, 10^9, d=(m - 1)%9 + 1; if (m%d == 0, write("b064807.txt", n++, " ", m); if (n==1000, return)) ) \\ Harry J. Smith, Sep 26 2009
(PARI) is(n)=n%((n-1)%9+1)==0 \\ Charles R Greathouse IV, Dec 26 2013
(Haskell)
a064807 n = a064807_list !! (n-1)
a064807_list = filter (\x -> x `mod` a010888 x == 0) [1..]
-- Reinhard Zumkeller, Jan 03 2014
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
Reinhard Zumkeller, Oct 21 2001
EXTENSIONS
Offset changed from 0 to 1 by Harry J. Smith, Sep 26 2009
STATUS
approved