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A034017 Numbers that are primitively represented by x^2 + xy + y^2. 11
0, 1, 3, 7, 13, 19, 21, 31, 37, 39, 43, 49, 57, 61, 67, 73, 79, 91, 93, 97, 103, 109, 111, 127, 129, 133, 139, 147, 151, 157, 163, 169, 181, 183, 193, 199, 201, 211, 217, 219, 223, 229, 237, 241, 247, 259, 271, 273, 277, 283, 291, 301, 307, 309, 313, 327, 331 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Gives the location of the nonzero terms of A000086.

Starting at a(3), a(n)^2 is the ordered semiperimeter of primitive integer Soddyian triangles (see A210484). - Frank M Jackson, Feb 04 2013

A000086(a(n)) > 0; a(n) = A004611(k) or a(n) = 3*A004611(k) for n > 3 and an appropriate k. - Reinhard Zumkeller, Jun 23 2013

The number of structure units in an icosahedral virus is 20*a(n)*k^2 for integers n and k, see Stannard link. - Charles R Greathouse IV, Nov 03 2015

REFERENCES

B. C. Berndt and R. A. Rankin, Ramanujan: Letters and Commentary, see p. 184, AMS, Providence, RI, 1995.

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)

Linda Stannard, Principles of Virus Architecture (archived version)

FORMULA

3^{0 or 1} X product of primes of form 3a+1 to any power.

MAPLE

N:= 1000: # to get all terms <= N

P:= select(isprime, [seq(6*n+1, n=1..floor((N-1)/6))]):

A:= {1, 3}:

for p in P do

  A:= {seq(seq(a*p^k, k=0..floor(log[p](N/a))), a=A)}:

od:

sort(convert(A, list)); # Robert Israel, Nov 04 2015

MATHEMATICA

lst = {0}; maxLen = 331; Do[If[Reduce[m^2 + m*n + n^2 == k && m >= n >= 0 && GCD[m, n] == 1, {m, n}, Integers] === False, , AppendTo[lst, k]], {k, maxLen}]; lst (* Frank M Jackson, Jan 10 2013 *) (* simplified by T. D. Noe, Feb 05 2013 *)

PROG

(PARI) is(n)=my(f=factor(n)); for(i=1, #f[, 1], if(f[i, 1]%3!=1 && (f[i, 1]!=3 || f[i, 2]>1), return(n==0))); 1 \\ Charles R Greathouse IV, Jan 10 2013

(Haskell)

a034017 n = a034017_list !! (n-1)

a034017_list = 0 : filter ((> 0) . a000086) [1..]

-- Reinhard Zumkeller, Jun 23 2013

CROSSREFS

Cf. A003136, A045611, A045897, A226946 (complement), A045897 (subsequence).

Sequence in context: A310259 A118667 A258117 * A034021 A216516 A310260

Adjacent sequences:  A034014 A034015 A034016 * A034018 A034019 A034020

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

EXTENSIONS

Extended by Ray Chandler, Jan 29 2009

STATUS

approved

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Last modified January 23 22:16 EST 2020. Contains 331177 sequences. (Running on oeis4.)