A339933 Number of partitions of n into two parts with the same sum of divisors.

0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 2, 0, 1, 1, 1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 1, 0, 1, 1, 2, 0, 1, 0, 1, 2, 2, 0, 1, 0, 1, 0, 1, 0, 2, 0, 1, 0, 2, 1, 2, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1

Offset

1,38

Links

Table of n, a(n) for n=1..94.

Index entries for sequences related to partitions

Formula

a(n) = Sum_{k=1..floor(n/2)} [sigma(k) = sigma(n-k)], where [ ] is the Iverson bracket and sigma(n) is the sum of divisors of n (A000203).

Example

a(38) = 2; There are two partitions of 38 into two parts with the same sum of divisors, (23,15) and (19,19), since 1+23 = 24 = 1+3+5+15 and 1+19 = 20 = 1+19.

Mathematica

Table[Sum[KroneckerDelta[DivisorSigma[1, i], DivisorSigma[1, n - i]], {i, Floor[n/2]}], {n, 100}]

Crossrefs

Cf. A000203.

Sequence in context: A076754 A346482 A364043 * A101659 A359823 A373336

Adjacent sequences: A339930 A339931 A339932 * A339934 A339935 A339936

Keyword

nonn

Author

Wesley Ivan Hurt, Dec 23 2020

Status

approved