

A337944


Total number of divisors of the sum of the squared parts in each partition of n into two parts.


1



0, 2, 2, 8, 4, 16, 7, 24, 14, 26, 14, 50, 18, 47, 24, 60, 23, 84, 30, 72, 45, 80, 37, 140, 36, 92, 64, 135, 46, 144, 53, 152, 84, 127, 59, 238, 62, 156, 100, 180, 71, 263, 76, 230, 110, 189, 85, 352, 102, 194, 133, 254, 98, 346, 98, 333, 162, 256, 114, 408, 118, 273, 201, 360
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OFFSET

1,2


LINKS

Table of n, a(n) for n=1..64.


FORMULA

a(n) = Sum_{i=1..floor(n/2)} d(i^2 + (ni)^2), where d(n) is the number of divisors of n (A000005).


EXAMPLE

a(6) = 16; 6 has 3 partitions into two parts, (5,1), (4,2) and (3,3). The sums of the squared parts from each partition are 5^2 + 1^2 = 26, 4^2 + 2^2 = 20 and 3^2 + 3^2 = 18. Then d(26) + d(20) + d(18) = 4 + 4 + 8 = 16.


MATHEMATICA

Table[Sum[DivisorSigma[0, i^2 + (n  i)^2], {i, Floor[n/2]}], {n,
100}]


CROSSREFS

Cf. A000005, A337943.
Sequence in context: A144847 A143625 A003612 * A103839 A135727 A320423
Adjacent sequences: A337941 A337942 A337943 * A337945 A337946 A337947


KEYWORD

nonn


AUTHOR

Wesley Ivan Hurt, Oct 01 2020


STATUS

approved



