OFFSET
1,3
COMMENTS
The exponents cannot all be zero.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..1000
FORMULA
G.f.: Sum_{k>=1} 1/(Product_{r>=0} 1-x^(prime(k)^r)) - 1/(1-x). - Andrew Howroyd, Dec 29 2017
EXAMPLE
a(5)=5: 5^1, 3^1+2*3^0, 2^2+1, 2*2^1+1, 2^1+3*2^0
From Gus Wiseman, Oct 10 2018: (Start)
The a(2) = 1 through a(9) = 15 integer partitions:
(2) (3) (4) (5) (33) (7) (8) (9)
(21) (22) (41) (42) (331) (44) (81)
(31) (221) (51) (421) (71) (333)
(211) (311) (222) (511) (422) (441)
(2111) (411) (2221) (2222) (711)
(2211) (4111) (3311) (4221)
(3111) (22111) (4211) (22221)
(21111) (31111) (5111) (33111)
(211111) (22211) (42111)
(41111) (51111)
(221111) (222111)
(311111) (411111)
(2111111) (2211111)
(3111111)
(21111111)
(End)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], PrimePowerQ[Times@@#]&]], {n, 30}] (* Gus Wiseman, Oct 10 2018 *)
PROG
(PARI) first(n)={Vec(sum(k=2, n, if(isprime(k), 1/prod(r=0, logint(n, k), 1-x^(k^r) + O(x*x^n)) - 1/(1-x), 0)), -n)} \\ Andrew Howroyd, Dec 29 2017
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Marc LeBrun, Sep 20 2001
EXTENSIONS
Name clarified by Andrew Howroyd, Dec 29 2017
STATUS
approved