

A334409


Numbers m such that the sum of the first k divisors and the last k divisors of m is equal to 2*m for some k that is smaller than half of the number of divisors of m.


1



36, 152812, 6112576, 72702928, 154286848, 397955025, 15356519488, 23003680492, 35755623784, 93789539668, 302122464256, 351155553970, 1081806148665, 1090488143872, 1663167899025, 2233955122576
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OFFSET

1,1


COMMENTS

If k is allowed to be equal to half of the number of divisors of m, then the perfect numbers (A000396) will be terms.
a(17) > 10^13. 3021194449732665786499072 is also a term.  Giovanni Resta, May 09 2020


LINKS

Table of n, a(n) for n=1..16.


EXAMPLE

36 is a term since its divisors are {1, 2, 3, 4, 6, 9, 12, 18, 36} and the sum of the first 3 and last 3 divisors is (1 + 2 + 3) + (12 + 18 + 36) = 72 = 2 * 36.


MATHEMATICA

seqQ[n_] := Module[{d = Divisors[n]}, nd = Length[d]; nd2 = Ceiling[nd/2]  1; s = Accumulate[d[[1 ;; nd2]] + n/d[[1 ;; nd2]]]; MemberQ[s, 2*n]]; Select[Range[10^6], seqQ]


CROSSREFS

Subsequence of A005835 and A334405.
A variant of A194472 and A318168.
Cf. A000396, A334410.
Sequence in context: A133015 A203270 A185960 * A216832 A013839 A271386
Adjacent sequences: A334406 A334407 A334408 * A334410 A334411 A334412


KEYWORD

nonn,more


AUTHOR

Amiram Eldar, Apr 27 2020


EXTENSIONS

a(8)a(16) from Giovanni Resta, May 06 2020


STATUS

approved



