A260152 a(n) is the number of distinct sums s + t where s, t are divisors of n.

1, 3, 3, 6, 3, 9, 3, 10, 6, 10, 3, 16, 3, 10, 9, 15, 3, 19, 3, 20, 10, 10, 3, 26, 6, 10, 10, 20, 3, 28, 3, 21, 10, 10, 10, 33, 3, 10, 10, 32, 3, 32, 3, 21, 18, 10, 3, 40, 6, 21, 10, 21, 3, 33, 10, 32, 10, 10, 3, 50, 3, 10, 20, 28, 10, 33, 3, 21, 10, 34

Offset

1,2

Comments

s and t need not be distinct.

a(n) = 3 if and only if n is prime.

If p is prime, a(p^k) = A000217(k+1).

If p is in A005382, a(p*(2*p-1)) = 9. For all other members of A006881, a(n) = 10.

a(n) <= A000217(A000005(n)).

Links

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

MathOverflow, A different kind of divisor sums

Example

For n = 2 the divisors are 1 and 2, and the a(2) = 3 distinct sums are 1+1=2, 1+2=3, 2+2=4.

Maple

T:= proc(n) local D, x, y;
  D:= numtheory:-divisors(n);
  nops({seq(seq(x+y, x=D), y=D)})
end proc:
seq(T(n), n=1..100);

Prog

(PARI) a(n) = my(v=[], d = divisors(n)); for (i=1, #d, for (j=i, #d, v = concat(v, d[i]+d[j]))); #Set(v); \\ Michel Marcus, Aug 29 2018

Crossrefs

Cf. A000005, A000217, A005382, A006881, A007425.

Cf. A048691 (with distinct products s*t rather than sums).

Sequence in context: A226602 A307000 A007425 * A358223 A130695 A308083

Adjacent sequences: A260149 A260150 A260151 * A260153 A260154 A260155

Keyword

nonn

Author

Robert Israel, Nov 09 2015

Status

approved