login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A340728 a(n) is the number of divisors d of n such that n/d - d is prime. 2
0, 0, 1, 1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 2, 1, 0, 0, 3, 0, 1, 0, 0, 0, 3, 0, 1, 0, 1, 0, 3, 0, 1, 0, 0, 1, 1, 0, 2, 0, 1, 0, 3, 0, 2, 0, 0, 0, 3, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 4, 0, 2, 1, 0, 0, 3, 0, 2, 0, 1, 0, 1, 0, 1, 0, 0, 0, 3, 0, 3, 0, 0, 0, 3, 0, 1, 0, 1, 0, 3, 0, 1, 0, 0, 0, 1, 0, 3, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,8
COMMENTS
If n is odd, then a(n) = 0 unless n is in A000466, in which case a(n) = 1.
LINKS
FORMULA
a(n) = Sum_{d|n} c(n/d-d), where c is the prime characteristic (A010051). - Wesley Ivan Hurt, Jan 18 2021
EXAMPLE
a(8) = 2; among the divisors {1,2,4,8} of 8, there are two cases where 8/d-d is prime: 8/1-1 = 7 and 8/2-2 = 2.
MAPLE
f:= proc(n) local D, i, m;
D:= sort(convert(numtheory:-divisors(n), list));
m:= nops(D);
nops(select(i -> isprime(D[m+1-i]-D[i]), [$1..(m+1)/2]));
end proc:
map(f, [$1..100]);
PROG
(PARI) a(n) = sumdiv(n, d, isprime(n/d-d)); \\ Michel Marcus, Jan 18 2021
CROSSREFS
Sequence in context: A363854 A353967 A035169 * A275851 A067432 A364011
KEYWORD
nonn
AUTHOR
J. M. Bergot and Robert Israel, Jan 17 2021
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)