OFFSET
1,1
COMMENTS
Promic numbers are highly divisible, so most of them are abundant.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
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
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