OFFSET
0,7
COMMENTS
All parts are greater than 1, there are at least two parts, and each part size has the same multiplicity.
This sequence was inspired by a post of Ali Sada, May 7 2020 on the seqfan mailing list.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..1000
FORMULA
a(n) = -1 + Sum_{d|n} A025147(d) for n > 1. - Andrew Howroyd, May 07 2020
EXAMPLE
The a(4) = 1 partition is 2 + 2.
The a(7) = 2 partitions are 2 + 5 and 3 + 4. Each part has multiplicity 1.
MATHEMATICA
Table[Length@Select[IntegerPartitions[n], Min[#] > 1 && Length[#] > 1 && (Length[Union[Length /@ Split[Sort[#]]]] == 1) &], {n, 0, 20}]
PROG
(PARI) \\ here b(n) is A025147.
b(n)={my(A=O(x*x^n)); polcoef(eta(x^2 + A) / eta(x + A) / (1 + x), n)}
a(n)={if(n<=1, 0, sumdiv(n, d, b(d)) - 1)} \\ Andrew Howroyd, May 07 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Olivier Gérard, May 07 2020
STATUS
approved