A362832 Number of partitions of n into two distinct parts (s,t) such that phi(s) = phi(t).

0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 2, 1, 1, 0, 0, 1, 1, 2, 1, 0, 3, 1, 1, 0, 0, 2, 1, 0, 3, 1, 0, 0, 0, 1, 1, 1, 2, 1, 0, 1, 2, 1, 0, 1, 1, 2, 1, 0, 2, 1, 0, 2, 1, 1, 1, 1, 0, 0, 2, 1, 0, 0, 3

Offset

1,39

Links

Table of n, a(n) for n=1..91.

Index entries for sequences related to partitions

Formula

a(n) = Sum_{k=1..floor((n-1)/2)} [phi(k) = phi(n-k)], where [ ] is the Iverson bracket and phi is the Euler totient function (A000010).

a(n) = (A362719(n-1) - ((n-1) mod 2))/2.

Example

a(49) = 3. The 3 partitions of 49 are (13,36), (17,32), and (21,28).

Mathematica

Table[Sum[KroneckerDelta[EulerPhi[k], EulerPhi[n - k]], {k, Floor[(n - 1)/2]}], {n, 100}]

Crossrefs

Cf. A000010 (phi), A362719.

Sequence in context: A359249 A284996 A215029 * A368751 A025908 A134404

Adjacent sequences: A362829 A362830 A362831 * A362833 A362834 A362835

Keyword

nonn,easy

Author

Wesley Ivan Hurt, May 04 2023

Status

approved