

A316221


Let S(n) = set of divisors of n, excluding n; sequence gives n such that there is a unique relatively prime subset of S(n) that sums to n.


0



6, 12, 18, 20, 28, 42, 54, 56, 66, 88, 100, 104, 162, 176, 196, 208, 272, 304, 368, 414, 460, 464, 486, 490, 496, 500, 558, 572, 580, 650, 666, 726, 736, 748, 812, 820, 868, 928, 968, 992, 1036, 1148, 1184, 1204, 1312, 1316, 1352, 1372, 1376, 1458, 1484, 1504
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OFFSET

1,1


COMMENTS

The relatively prime condition arises naturally from the perspective of Egyptian fractions representations of unity which in turn arise upon dividing the elements of such a subset all by n. In particular the condition guarantees that the Egyptian fraction representation of unity doesn't arise already from any smaller n.


LINKS



EXAMPLE

6=1+2+3, 12=1+2+3+6, 18=1+2+6+9, 20=1+4+5+10, 28=1+2+4+7+14, 42=1+6+14+21.


MATHEMATICA

ric[r_, g_, p_] := Block[{v}, If[r==0, If[g==1, c++], If[c<2 && Total@p >= r, ric[r, g, Rest@ p]; v = p[[1]]; If[r>=v, ric[rv, GCD[g, v], Rest@ p]]]]]; ok[n_] := DivisorSigma[1, n] >= 2 n && (c = 0; ric[n, n, Reverse@ Most@ Divisors@ n]; c == 1); Select[ Range[2000], ok] (* Giovanni Resta, Jun 27 2018 *)


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



