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.

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

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. Adams-Watters, 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: A347056 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. Adams-Watters, Dec 18 2006

Status

approved