OFFSET
0,8
COMMENTS
All parts are greater than 1, there is more than one part, 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) - 1) for n > 0. - Andrew Howroyd, May 07 2020
EXAMPLE
The a(10) = 5 partitions are 2 + 8, 3 + 7, 4 + 6, 2 + 3 + 5 and 2 + 2 + 3 + 3.
MATHEMATICA
Table[Length@Select[IntegerPartitions[n], Min[#] > 1 && Length[#] > 1 && Length[Union[#]] > 1 && (Length[Union[Length /@ Split[Sort[#]]]] == 1) &], {n, 0, 40}]
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, 1 + sumdiv(n, d, b(d)-1))} \\ Andrew Howroyd, May 07 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Olivier Gérard, May 07 2020
STATUS
approved