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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

Robert Israel, Table of n, a(n) for n = 1..10000

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

Cf. A000466, A010051, A179993, A340729.

Sequence in context: A178112 A324852 A035169 * A275851 A067432 A192174

Adjacent sequences:  A340725 A340726 A340727 * A340729 A340730 A340731

KEYWORD

nonn

AUTHOR

J. M. Bergot and Robert Israel, Jan 17 2021

STATUS

approved

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Last modified April 16 18:53 EDT 2021. Contains 343050 sequences. (Running on oeis4.)