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.

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

Offset: 1

Author

David V. Feldman, Jun 27 2018

Keywords

• nonn

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.

Examples

			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.
		

Crossrefs

Subsequence of A005835. Related to A064771.

Programs

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[r-v, 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 *)

Extensions

More terms from Giovanni Resta, Jun 27 2018