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

1,2

Comments

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.

Links

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

Example

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.

Crossrefs

Cf. A025426, A054994, A274567.

Sequence in context: A109616 A181785 A018262 * A018356 A026383 A162963

Adjacent sequences: A336539 A336540 A336541 * A336543 A336544 A336545

Keyword

nonn

Author

David A. Corneth, Jul 24 2020

Status

approved