OFFSET
1,60
COMMENTS
As a simple consequence of the definition of a primitive nondeficient number, a(n) is nonzero if and only if n is nondeficient.
LINKS
FORMULA
a(n) = Sum_{d|n} A341619(d) = Sum_{d|n} [1==A341620(d)]. - Corrected by Antti Karttunen, Feb 21 2021
a(A005100(n)) = 0.
a(A006039(n)) = 1.
a(A023196(n)) >= 1.
a(n) <= A341620(n). - Antti Karttunen, Feb 22 2021
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Sum_{n>=1} 1/A006039(n) = 0.3... (see A006039 for a better estimate of this constant). - Amiram Eldar, Jan 01 2024
EXAMPLE
The least nondeficient number, therefore the least primitive nondeficient number is 6. So a(1) = a(2) = a(3) = a(4) = a(5) = 0 as all primitive nondeficient numbers are larger, and therefore not divisors; and a(6) = 1, as only 1 primitive nondeficient number divides 6, namely 6 itself.
60 has the following 12 divisors: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60. Of these, only 6 and 20 are in A006039, thus a(60) = 2.
PROG
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen and Peter Munn, Sep 15 2020
EXTENSIONS
Data section extended to 120 terms by Antti Karttunen, Feb 21 2021
STATUS
approved