

A293618


Numbers n that equal the sum of their first k consecutive aliquot biunitary divisors, but not all of them (i.e k < A286324(n)1).


2



24, 360, 432, 1344, 2016, 19440, 45360, 68544, 714240, 864000, 1468800, 1571328, 1900800, 2391120, 2888704, 3057600, 4586400, 5241600, 103194000
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OFFSET

1,1


COMMENTS

The biunitary version of ErdősNicolas numbers (A194472).
If all the aliquot biunitary divisors are permitted (i.e. k <= A286324(n)1), then the 3 biunitary perfect numbers, 6, 60 and 90, are included.


LINKS

Table of n, a(n) for n=1..19.


EXAMPLE

24 is in the sequence since its aliquot biunitary divisors are 1, 2, 3, 4, 6, 8, 12 and 24 and 1 + 2 + 3 + 4 + 6 + 8 = 24.


MATHEMATICA

f[n_] := Select[Divisors[n], Function[d, CoprimeQ[d, n/d]]]; bdiv[m_] := Select[Divisors[m], Last@Intersection[f@#, f[m/#]] == 1 &]; subtr = If[#1 < #2, Throw[#1], #1  #2] &; selDivs[n_] := Catch@Fold[subtr, n, Drop[bdiv[n], 2]]; a = {}; Do[ If[selDivs[n] == 0, AppendTo[a, n]; Print[n]], {n, 2, 10^6}]; a (* after Alonso del Arte at A194472 *)


CROSSREFS

Cf. A188999, A194472, A222266, A286324.
Sequence in context: A269029 A004325 A075621 * A137499 A122813 A028245
Adjacent sequences: A293615 A293616 A293617 * A293619 A293620 A293621


KEYWORD

nonn,more


AUTHOR

Amiram Eldar, Oct 13 2017


STATUS

approved



