A274567 -id:A274567 - cp's OEIS frontend

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

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.

A336543 a(n) is the number of ways to write A336542(n) as a sum of two nonzero squares.

Original entry on oeis.org

0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 2, 3, 4, 3, 4, 4, 3, 4, 4, 6, 3, 5, 5, 6, 3, 5, 6, 8, 4, 8, 6, 6, 8, 8, 9, 4, 6, 7, 10, 9, 4, 12, 7, 8, 8, 10, 12, 12, 4, 7, 9, 8, 12, 12, 5, 16, 8, 9, 16, 13, 10, 12, 16, 15, 5, 8, 18, 16, 14, 10, 10, 14, 15, 5, 20, 18, 16, 9, 11

Offset: 1

David A. Corneth, Jul 24 2020

nonn

			a(11) = 3 as A336542 = 325 and can be written in three ways as a sum of two nonzero squares.

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

Cf. A025426, A274567.

a(n) = A025426(A336542(n)). - Michel Marcus, Jul 31 2020

cp's OEIS Frontend

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

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