

A092933


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.


3



1, 3, 4, 6, 16, 20, 24, 27, 54, 64, 80, 96, 120, 216, 243, 252, 256, 272, 320, 384, 410, 465, 480, 486, 500, 637, 715, 732, 864, 936, 1008, 1024, 1080, 1088, 1280, 1435, 1536, 1586, 1632, 1920, 1944, 2000, 2052, 2065, 2187, 2200, 2268, 2280, 3000, 3164, 3456
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OFFSET

1,2


COMMENTS

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. AdamsWatters, Dec 18 2006


LINKS

Amiram Eldar, Table of n, a(n) for n = 1..2000


EXAMPLE

6 is a member as 6 = 1 + 5. 16 is also a member.
The numbers coprime to 16 are 1, 3, 5, 7, 9, 11, 13, 15. The partial sums are 1, 4, 9, 16, 25,...


MATHEMATICA

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


CROSSREFS

Cf. A117892, A117893.
Sequence in context: A122727 A089249 A173944 * A122849 A068573 A138577
Adjacent sequences: A092930 A092931 A092932 * A092934 A092935 A092936


KEYWORD

nonn


AUTHOR

Amarnath Murthy, Mar 22 2004


EXTENSIONS

More terms from Franklin T. AdamsWatters, Dec 18 2006


STATUS

approved



