OFFSET
1,4
COMMENTS
a(n) is also the number of partitions of n with at least one distinct part (i.e., not all parts are equal).
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..1000
Omar E. Pol, The shell model of partitions
MAPLE
with(numtheory): b:= proc(n) option remember; `if`(n=0, 1, add(add(d, d=divisors(j)) *b(n-j), j=1..n)/n) end: a:= n-> b(n)- tau(n):
seq(a(n), n=1..50); # Alois P. Heinz, Oct 07 2008
MATHEMATICA
Table[PartitionsP[n]-DivisorSigma[0, n], {n, 50}] (* Harvey P. Dale, Apr 10 2014 *)
PROG
(PARI) al(n)=vector(n, k, numbpart(k)-numdiv(k))
(Python)
from sympy import npartitions, divisor_count
def A144300(n): return npartitions(n)-divisor_count(n) # Chai Wah Wu, Oct 16 2023
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Omar E. Pol, Sep 17 2008
STATUS
approved