A006308 -id:A006308 - cp's OEIS frontend

A372933 Records in A071961, divided by 2.

0, 1, 2, 3, 4, 10, 21, 27, 55, 78, 136, 171, 253, 406, 465, 666, 820, 903, 1081, 1378, 1711, 1830, 2211, 2485, 2628, 3081, 3403, 3916, 4656, 5050, 5253, 5671, 5886, 6328, 6655, 8001, 8515, 9316, 9591, 11026, 11325, 12246, 13203, 13861, 14878, 15931, 16290, 18145, 18528

Offset: 1

Hugo Pfoertner, May 17 2024

nonn

A372934 are the corresponding positions in A071961.
Cf. A372728.
Cf. A006308, A008837.

a372933(upto) = {my (m=-oo); for (n=0, 2*upto, my (s = sum(k=0, n, kronecker(n,k))); if (s>m, print1(s/2,", "); m=s))};
a372933(10000)

A006311 Coefficients of period polynomials.

Original entry on oeis.org

-3, 10, -84, -10989, 363883, -82620, -137550709, 645413252986, -7142036935967, -7522164033404415, -217498966742521653325, -10590850429623318361311, 14571491290875996179048369, -5355885371863393108886638462583

Offset: 2

N. J. A. Sloane

sign

D. H. and Emma Lehmer, Cyclotomy for nonsquarefree moduli, pp. 276-300 of Analytic Number Theory (Philadelphia 1980), Lect. Notes Math. 899 (1981).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Sean A. Irvine, Table of n, a(n) for n = 2..26

a(n) = [x^1] f(p,x) where p = A000040(n) and f(p,x) is defined in A006308. - Sean A. Irvine, Mar 08 2017

More terms, signs added, and offset corrected by Sean A. Irvine, Mar 08 2017

A061591 a(n) = 2^x, where x = p*(p-1)/2 and p is the n-th prime.

Original entry on oeis.org

2, 8, 1024, 2097152, 36028797018963968, 302231454903657293676544, 87112285931760246646623899502532662132736, 2993155353253689176481146537402947624255349848014848

Offset: 1

Labos Elemer, May 22 2001

nonn

Harry J. Smith, Table of n, a(n) for n = 1..22

Cf. A007955, A006308. The exponents x are in A008837.

Table[2^((p(p-1))/2),{p,Prime[Range[10]]}] (* Harvey P. Dale, Sep 03 2024 *)

{ n=0; forprime (p=2, prime(22), write("b061591.txt", n++, " ", 2^(p*(p - 1)/2)) ) } \\ Harry J. Smith, Jul 25 2009

Offset changed from 2 to 1 by Harry J. Smith, Jul 25 2009

A006309 Coefficients of period polynomials.

Original entry on oeis.org

1, 5, -21, 33, -65, 85, -133, 161, 261, -341, -481, 533, -645, 705, 901, -12803, -1281, -1541, 1633, -1825, -14615, -11537, 2581, -3201, 3333

Offset: 2

N. J. A. Sloane

D. H. and Emma Lehmer, Cyclotomy for nonsquarefree moduli, pp. 276-300 of Analytic Number Theory (Philadelphia 1980), Lect. Notes Math. 899 (1981).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

David Naccache and Ofer Yifrach-Stav, Pattern Recognition Experiments on Mathematical Expressions, arXiv:2301.01624 [math.NT], 2022.
Ofer Yifrach-Stav, Fast and Private Pool Testing and Contributions to Experimental Mathematics, Doctoral thesis, École normale supérieure (Paris, France), HAL Science [math.cs] 2024, Art. No. tel-04513104. See pp. 108, 109, 212.

a(n) = [x^(p-3)] f(p,x) where p = A000040(n) and f(p,x) is defined in A006308. - Sean A. Irvine, Mar 07 2017

More terms, signs added, and offset corrected by Sean A. Irvine, Mar 07 2017

cp's OEIS Frontend

A372933 Records in A071961, divided by 2.

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A006311 Coefficients of period polynomials.

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A061591 a(n) = 2^x, where x = p*(p-1)/2 and p is the n-th prime.

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A006309 Coefficients of period polynomials.

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