A054994 -id:A054994 - cp's OEIS frontend

A344470 Record values in A002654.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 20, 24, 32, 36, 40, 48, 64, 72, 80, 96, 128, 144, 160, 192, 216, 256, 288, 320, 384, 432, 512, 576, 640, 768, 864, 960, 1024, 1152, 1280, 1536, 1728, 1920, 2048, 2304, 2560, 2880, 3072, 3456, 3840, 4096, 4608, 5120, 5760, 6144

Offset: 1

Jianing Song, May 20 2021

nonn

Also numbers k such that A018782(m) > A018782(k) for all m > k.

			9 is a term because the circle with radius sqrt(4225) centered at the origin hits exactly 4*9 = 36 integer points, and any circle with radius < sqrt(4225) centered at the origin hits fewer than 36 points.

Jianing Song, Table of n, a(n) for n = 1..424

Cf. A071383, A071385, A002654, A018782, A000005, A054994.

Records of Sum_{d|n} kronecker(m, d): A344472 (m=-3), this sequence (m=-4), A279542 (m=-6).

my(v=list(10^15), rec=0); for(n=1, #v, if(numdiv(v[n])>rec, rec=numdiv(v[n]); print1(rec, ", "))) \\ see program for A054994

a(n) = A071385(n+1)/4.

a(n) = A000005(A071383(n+1)) = A002654(A071383(n+1)).

A274567 Least number k such that k^2-1 is the sum of two nonzero squares in exactly n ways.

Original entry on oeis.org

3, 81, 51, 291, 1251, 339, 62499, 1971, 5201, 5001, 175781251, 7299

Offset: 1

Altug Alkan, Jun 28 2016

a(11) > 25*10^5 if it exists. - Chai Wah Wu, Jul 23 2020
From David A. Corneth, Jul 23 2020: (Start)
a(13) <= 17578125001, a(17) <= 610351562499. (End)

			a(2) = 81 because 81^2 - 1 = 28^2 + 76^2 = 44^2 + 68^2.

Cf. A000404, A005563, A016032, A025426, A050795, A050797, A054994.

a(10) from Chai Wah Wu, Jul 22 2020

A336542 Primitive integers for the number of ways k to write as a sum of two squares.

Original entry on oeis.org

1, 2, 5, 10, 25, 50, 65, 125, 130, 250, 325, 625, 650, 1105, 1250, 1625, 2210, 3125, 3250, 4225, 5525, 6250, 8125, 8450, 11050, 15625, 16250, 21125, 27625, 31250, 32045, 40625, 42250, 55250, 64090, 71825, 78125, 81250, 105625, 138125, 143650, 156250, 160225, 203125, 211250

Offset: 1

David A. Corneth, Jul 24 2020

nonn

The number of ways to write k as a number of two squares only depends on the parity of the multiplicity of 2, the parity of the multiplicity of a prime of the form 4*m + 3 and the multiplicity of a prime of the form 4*m+1 (See A025426). Terms in this sequence have no prime factors of the form 4*m + 3.

			650 = 2*5*13 is in the sequence as its prime factors are 2 or of the form 4*m + 1. It's the least positive integer of the form 2*p*q where p and q are distinct and each of the form 4*m+1.

David A. Corneth, Table of n, a(n) for n = 1..10000

Cf. A025426, A054994, A274567.

cp's OEIS Frontend

A344470 Record values in A002654.

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A274567 Least number k such that k^2-1 is the sum of two nonzero squares in exactly n ways.

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A336542 Primitive integers for the number of ways k to write as a sum of two squares.

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