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A124672 Pronic (oblong) 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

Pronic numbers are highly divisible, so most of them are abundant.

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

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 *)

CROSSREFS

Intersection of A002378 (oblong numbers) and A005101 (abundant numbers).

Cf. A077804 (deficient oblong numbers).

Sequence in context: A210968 A107277 A256883 * A289980 A109547 A269453

Adjacent sequences:  A124669 A124670 A124671 * A124673 A124674 A124675

KEYWORD

nonn

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

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Last modified August 21 05:37 EDT 2019. Contains 326162 sequences. (Running on oeis4.)