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A336542 Primitive integers for the number of ways k to write as a sum of two squares. 2
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 (list; graph; refs; listen; history; text; internal format)
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:  A336538 A336539 A336540 * A336543 A336544 A336545

KEYWORD

nonn

AUTHOR

David A. Corneth, Jul 24 2020

STATUS

approved

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Last modified September 21 12:49 EDT 2020. Contains 337272 sequences. (Running on oeis4.)