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 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified November 29 03:03 EST 2023. Contains 367422 sequences. (Running on oeis4.)