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A339933
Number of partitions of n into two parts with the same sum of divisors.
0
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
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
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Dec 23 2020
STATUS
approved