

A194472


ErdÅ‘sNicolas numbers


1



24, 2016, 8190, 42336, 45864, 392448, 714240, 1571328, 61900800, 91963648, 211891200, 1931236608, 2013143040, 4428914688, 10200236032, 214204956672
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OFFSET

1,1


COMMENTS

Abundant numbers n such that the sum of the first k divisors is equal to n for some k, thus this is a subsequence of A064510. k has to be less than tau(n)  1 for this sequence, whereas in A064510 k = tau(n)  1 is allowed (and thus perfect numbers are in that sequence).
a(17) > 5*10^11. 104828758917120, 916858574438400, 967609154764800, 93076753068441600, 215131015678525440 and 1371332329173024768 are also terms.  Donovan Johnson, Dec 26 2012
a(17) > 10^12.  Giovanni Resta, Apr 15 2017


REFERENCES

J.M. De Koninck, Those Fascinating Numbers, Amer. Math. Soc., (2009): 141


LINKS

Table of n, a(n) for n=1..16.
P. Erdos and J.L. Nicolas, Repartition des nombres superabondants, Bull. Soc. Math. France 103 (1975) no. 1, pp. 6590.


EXAMPLE

The divisors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24 and 1 + 2 + 3 + 4 + 6 + 8 = 24, hence 24 is in the list.
The divisors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. The first seven of these add up to 36, but the first eight add up to 52, therefore 48 is not on the list.


MATHEMATICA

subtr = If[#1 < #2, Throw[#1], #1  #2] &; selDivs[n_] := Catch@Fold[subtr, n, Drop[Divisors[n], 2]]; erdNickNums = {}; Do[If[selDivs[n] == 0, AppendTo[erdNickNums, n]], {n, 2, 10^5}]; erdNickNums (* Based on the program by Bobby R. Treat and Robert G. Wilson v for A064510 *)


CROSSREFS

Cf. A005835, A000396, A064510.
Sequence in context: A262010 A267075 A263605 * A246602 A001501 A054005
Adjacent sequences: A194469 A194470 A194471 * A194473 A194474 A194475


KEYWORD

nonn


AUTHOR

Alonso del Arte, Aug 24 2011


EXTENSIONS

More terms from M. F. Hasler, Aug 24 2011


STATUS

approved



