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

1,1

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

Table of n, a(n) for n=1..52.

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[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 *)

Crossrefs

Subsequence of A005835. Related to A064771.

Sequence in context: A228870 A291022 A348719 * A138939 A221220 A046411

Adjacent sequences: A316218 A316219 A316220 * A316222 A316223 A316224

Keyword

nonn

Author

David V. Feldman, Jun 27 2018

Extensions

More terms from Giovanni Resta, Jun 27 2018

Status

approved