login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A124672 Oblong (promic) abundant numbers = abundant numbers of the form k(k+1). 2
12, 20, 30, 42, 56, 72, 90, 132, 156, 210, 240, 272, 306, 342, 380, 420, 462, 552, 600, 650, 702, 756, 812, 870, 930, 992, 1056, 1122, 1190, 1260, 1332, 1482, 1560, 1640, 1722, 1806, 1980, 2070, 2256, 2352, 2450, 2550, 2652, 2862, 2970, 3080, 3192, 3306 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Promic numbers are highly divisible, so most of them are abundant.
LINKS
FORMULA
If k > 2 is 0 or 2 mod 3, then k*(k+1) is in this sequence; the bounds n^2 < a(n) < (9/4)*n^2 + 6n + 4 can be derived from this. Probably a(n) ~ kn^2 with k near 1.496. - Charles R Greathouse IV, Mar 16 2022
EXAMPLE
56 is in the sequence because 56=7*8 and the sum of its divisors 1+2+4+7+8+14+28+56=120 > 2*56.
MAPLE
with(numtheory): a:=proc(k) if sigma(k*(k+1))>2*k*(k+1) then k*(k+1) else fi end: seq(a(k), k=1..75); # Emeric Deutsch, Jan 01 2007
isA005101 := proc(n) if numtheory[sigma](n) > 2*n then RETURN(true) ; else RETURN(false) ; fi ; end : for k from 1 to 80 do if isA005101(k*(k+1)) then printf("%d, ", k*(k+1)) ; fi ; od ; # R. J. Mathar, Jan 07 2007
MATHEMATICA
s = {}; Do[ob = n*(n + 1); If[DivisorSigma[1, ob] > 2*ob, AppendTo[s, ob]], {n, 1, 100}]; s (* Amiram Eldar, Jun 07 2019 *)
PROG
(PARI) helper(n)=my(k=sqrtint(n)); if(k*(k+1)>n, k, k+1)
list(lim)=my(v=List(), last=4/3, cur); forfactored(n=4, helper(lim\1), cur=sigma(n, -1); if(cur*last>2, listput(v, (n[1]-1)*n[1])); last=cur); Vec(v) \\ Charles R Greathouse IV, Mar 16 2022
CROSSREFS
Intersection of A002378 (oblong numbers) and A005101 (abundant numbers).
Cf. A077804 (deficient oblong numbers).
Sequence in context: A210968 A107277 A256883 * A289980 A109547 A334418
KEYWORD
nonn,easy
AUTHOR
Tanya Khovanova, Dec 27 2006
EXTENSIONS
More terms from Emeric Deutsch, Jan 01 2007
More terms from R. J. Mathar, Jan 07 2007
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 12:59 EDT 2024. Contains 371254 sequences. (Running on oeis4.)