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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

%I #11 Jun 27 2018 15:51:45

%S 6,12,18,20,28,42,54,56,66,88,100,104,162,176,196,208,272,304,368,414,

%T 460,464,486,490,496,500,558,572,580,650,666,726,736,748,812,820,868,

%U 928,968,992,1036,1148,1184,1204,1312,1316,1352,1372,1376,1458,1484,1504

%N 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.

%C 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.

%e 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.

%t 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 *)

%Y Subsequence of A005835. Related to A064771.

%K nonn

%O 1,1

%A _David V. Feldman_, Jun 27 2018

%E More terms from _Giovanni Resta_, Jun 27 2018

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Last modified February 29 09:21 EST 2024. Contains 370418 sequences. (Running on oeis4.)