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Let 1, a, b, c,... be the numbers coprime to k in ascending order; then k belongs to this sequence if k = a partial sum of these numbers.
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%I #10 Feb 23 2020 06:42:11

%S 1,3,4,6,16,20,24,27,54,64,80,96,120,216,243,252,256,272,320,384,410,

%T 465,480,486,500,637,715,732,864,936,1008,1024,1080,1088,1280,1435,

%U 1536,1586,1632,1920,1944,2000,2052,2065,2187,2200,2268,2280,3000,3164,3456

%N Let 1, a, b, c,... be the numbers coprime to k in ascending order; then k belongs to this sequence if k = a partial sum of these numbers.

%C Sequence is infinite; it includes all powers of 4. More generally, if n is in this sequence, let i be the number just added to make the sum equal to n. If i+1 is divisible by every prime divisor of n, then n*m^2 is in the sequence for any number m whose prime divisors all divide n. This gives us subsequences 3*9^i, 6*4^i*9^j, 20*4^i*25^j, 120*4^i*9^j*25^k, etc. - _Franklin T. Adams-Watters_, Dec 18 2006

%H Amiram Eldar, <a href="/A092933/b092933.txt">Table of n, a(n) for n = 1..2000</a>

%e 6 is a member as 6 = 1 + 5. 16 is also a member.

%e The numbers coprime to 16 are 1, 3, 5, 7, 9, 11, 13, 15. The partial sums are 1, 4, 9, 16, 25,...

%t seqQ[n_] := MemberQ[Accumulate @ Select[Range[n], CoprimeQ[n, #] &], n]; Select[Range[3500], seqQ] (* _Amiram Eldar_, Feb 23 2020 *)

%Y Cf. A117892, A117893.

%K nonn

%O 1,2

%A _Amarnath Murthy_, Mar 22 2004

%E More terms from _Franklin T. Adams-Watters_, Dec 18 2006