A018261 -id:A018261 - cp's OEIS frontend

A034668 Sum of n-th powers of divisors of 48.

10, 124, 3410, 131068, 5732210, 264105844, 12441770330, 591961476748, 28294099221410, 1355321291969764, 64989628053819050, 3117943006504850428, 149624153907514522610, 7181073568202394620884, 344670347564106497096570

Offset: 0

N. J. A. Sloane

T. D. Noe, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (124,-5983,150040,-2180788,19254592,-104677824,345692160,-661671936,658243584,-254803968).

Cf. A018261 (divisors of 48).

[DivisorSigma(n,48): n in [0..15]]; // Vincenzo Librandi, Apr 17 2014

With[{d=Divisors[48]},Table[Total[d^n],{n,0,20}]] (* Harvey P. Dale, Aug 14 2012 *)
Total[#^Range[0, 20]&/@Divisors[48]] (* Vincenzo Librandi, Apr 17 2014 *)

a(n) = Sum_{d|48} d^n. - Wesley Ivan Hurt, Dec 29 2023

A018276 Divisors of 84.

Original entry on oeis.org

1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84

Offset: 1

N. J. A. Sloane

Index entries for sequences related to divisors of numbers

Cf. A018261, A018271.

Divisors[84] (* Vladimir Joseph Stephan Orlovsky, Feb 16 2012 *)

divisors(84) \\ Charles R Greathouse IV, Jun 21 2017

A018259 Divisors of 44.

Original entry on oeis.org

1, 2, 4, 11, 22, 44

Offset: 1

N. J. A. Sloane

Index entries for sequences related to divisors of numbers

Cf. A018253, A018256, A018261.

Divisors[44] (* Vladimir Joseph Stephan Orlovsky, Feb 16 2012 *)

divisors(44) \\ Charles R Greathouse IV, Jun 21 2017

A215068 Numbers n such that for all divisors d of n, d+1 is either a prime or a perfect power.

Original entry on oeis.org

1, 2, 3, 4, 6, 7, 8, 12, 16, 24, 31, 48, 127, 8191, 131071, 524287, 2147483647, 2305843009213693951, 618970019642690137449562111, 162259276829213363391578010288127, 170141183460469231731687303715884105727

Offset: 1

Joerg Arndt, Aug 02 2012

Apparently the divisors of 48 (A018261) together with the Mersenne primes (A000668).
Confirmed by Robert Israel, Aug 02 2020: see link.
Next term > 2*10^8.

Robert Israel, Proof of conjecture in A215068

Cf. A018261 (divisors of 48), A000668 (Mersenne primes), A001597 (perfect powers).

sort([op(numtheory:-divisors(48)), seq(numtheory:-mersenne([i]),i=2..12)]); # Robert Israel, Aug 02 2020

isA215068(n)=
{
    my(x);
    fordiv (n, d,
        d1 = d + 1;
        if ( isprime(d1) || ispower(d1), next() );
        return(0);
    );
    return(1);
}
for (n=1,10^9, if(isA215068(n), print1(n,", ")));

A367463 The orders, without repetition, of the subquotients of finite groups with irreducible representations in GL_4(Z).

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 16, 18, 20, 24, 32, 36, 40, 48, 60, 64, 72, 96, 120, 128, 144, 192, 240, 288, 384, 576, 1152

Offset: 1

Hal M. Switkay, Nov 18 2023

Conway and Sloane identify 5 conjugacy classes of maximal finite irreducible subgroups of GL_4(Z). Of these, 2 are isomorphic to subgroups of other groups in the list. The 3 maximal groups are: 1) the Weyl group of F4, the automorphism group of the D4 lattice, with order 1152; 2) the wreath square of the dihedral group of order 12, the automorphism group of the (A2)^2 lattice, with order 288; 3) the product of the symmetric group of degree 5 with the group of order 2, the automorphism group of the A4 lattice (and its dual), with order 240.

J. H. Conway and N. J. A. Sloane, Low-dimensional lattices. II. Subgroups of GL(n,Z), Proc. R. Soc. Lond. A 419 (1988), 29-68.

Cf. A018261.

A097071 Number of Shubnikov compounds.

Original entry on oeis.org

1, 2, 3, 5, 6, 10, 12, 18, 23, 30

Offset: 1

N. J. A. Sloane, Sep 15 2004

nonn

The definition is not clear to me.

According to the reference, this is meant to be the number of partitions of n into terms of A018261. So the correct value for a(9) is 22. - Andrey Zabolotskiy, Jul 11 2017

N. L. Smirnova and V. S. Urusov, Fundamental law of crystal symmetry by Shubnikov, its applications and restrictions, Computers and Mathematics with Applications, 16 (1988), 563-567.

A285660 Degree of the algebraic number sin(n degrees) = sin(n Pi/180 radians).

Original entry on oeis.org

1, 48, 12, 16, 24, 12, 4, 48, 24, 8, 3, 48, 8, 48, 12, 4, 24, 48, 2, 48, 6, 16, 12, 48, 8, 12, 12, 8, 24, 48, 1, 48, 24, 16, 12, 12, 4, 48, 12, 16, 6, 48, 4, 48, 24, 2, 12, 48, 8, 48, 3, 16, 24, 48, 2, 12, 24, 16, 12, 48, 2, 48, 12, 8, 24, 12, 4, 48, 24, 16, 3, 48, 4, 48, 12, 4, 24, 48, 4, 48, 6, 8, 12, 48, 8, 12, 12, 16, 24, 48, 1

Offset: 0

Rick L. Shepherd, Apr 23 2017

By definition, a(n) is the degree of the minimal polynomial of sin(n degrees).
Periodic sequence of period 360.
The sequence range is the set of all divisors of 48 (A018261), where 48 = Euler_phi(180) = A000010(180).
All 48 distinct algebraic numbers of degree 48 referenced here (i.e., where GCD(n, 180) = 1) have the same minimal polynomial, which is shown in A019810.

			sin(6 degrees) has minimal polynomial 16x^4 + 8x^3 - 16x^2 - 8x + 1 of degree 4, so a(6) = 4. sin(15 degrees) also has a minimal polynomial of degree 4 (but a different one, 16x^4 - 16x^2 + 1), so a(15) = 4.

Index entries for linear recurrences with constant coefficients, order 180.

Cf. A019810 (sin(1 degree)), A018261 (divisors of 48), A007775.

a(n) = a(n-360) for all n (extending the sequence to negative n).

cp's OEIS Frontend

A034668 Sum of n-th powers of divisors of 48.

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A018276 Divisors of 84.

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A018259 Divisors of 44.

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A215068 Numbers n such that for all divisors d of n, d+1 is either a prime or a perfect power.

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A367463 The orders, without repetition, of the subquotients of finite groups with irreducible representations in GL_4(Z).

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Author

Keywords

Comments

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Crossrefs

A097071 Number of Shubnikov compounds.

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A285660 Degree of the algebraic number sin(n degrees) = sin(n Pi/180 radians).

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