A210450 Numbers n such that 16n + 7 is in A192628.

0, 3, 4, 5, 6, 7, 11, 16, 17, 21, 23, 24, 27, 28, 32, 34, 35, 36, 38, 39, 40, 43, 44, 45, 47, 48, 49, 51, 53, 54, 55, 56, 59, 60, 63, 65, 67, 68, 69, 70, 72, 73, 74, 76, 77, 79, 81, 82, 85, 86, 89, 93, 96, 97, 98, 100, 102, 103, 105, 106, 107, 109, 110

Offset

1,2

Comments

Reduce the elements of A192718 (which are the elements of A192628 congruent to 7 (mod 16)) by subtracting 7 and dividing by 16. In "On the reciprocal of the binary generating function for the sum of divisors", this sequence is precisely the set T.

Links

Table of n, a(n) for n=1..63.

J. N. Cooper, D. Eichhorn, and K. O'Bryant, Reciprocals of binary power series, arXiv:math/0506496 [math.NT], 2005.

J. N. Cooper, D. Eichhorn, and K. O'Bryant, Reciprocals of binary power series, International Journal of Number Theory, 2 no. 4 (2006), 499-522.

J. N. Cooper and A. W. N. Riasanovsky, On the Reciprocal of the Binary Generating Function for the Sum of Divisors, 2012.

J. N. Cooper and A. W. N. Riasanovsky, On the Reciprocal of the Binary Generating Function for the Sum of Divisors, Journal of Integer Sequences, Vol. 16 (2013), #13.1.8.

Prog

(Sage)
prec = 2^12
R = PowerSeriesRing(GF(2), 'q', default_prec = prec)
q = R.gen()
sigma = lambda x : 1 if x == 0 else sum(Integer(x).divisors())
SigmaSeries = sum([sigma(m)*q^m for m in range(prec)])
SigmaBarSeries = 1/SigmaSeries
SigmaBarList = SigmaBarSeries.exponents()
reduced = [(m-7)/16 for m in SigmaBarList if mod(m, 8) == 7]
print(reduced[:128])

Crossrefs

Cf. A192718, A192628.

Sequence in context: A137922 A176984 A099562 * A133896 A052002 A247636

Adjacent sequences: A210447 A210448 A210449 * A210451 A210452 A210453

Keyword

nonn

Author

Alexander Riasanovsky, Jan 20 2013

Status

approved