A086665 Difference between sum of divisors of n and integer log of n, i.e., A000203(n) - A001414(n).

1, 1, 1, 3, 1, 7, 1, 9, 7, 11, 1, 21, 1, 15, 16, 23, 1, 31, 1, 33, 22, 23, 1, 51, 21, 27, 31, 45, 1, 62, 1, 53, 34, 35, 36, 81, 1, 39, 40, 79, 1, 84, 1, 69, 67, 47, 1, 113, 43, 81, 52, 81, 1, 109, 56, 107, 58, 59, 1, 156

Offset

1,4

Links

Table of n, a(n) for n=1..60.

Example

a(10) = sigma(10) - (2 + 5) = 1 + 2 + 5 + 10 - 7 = 11.

Mathematica

sigma1 = Table[Plus @@ Divisors[n], {n, 100}]; sopfr = Prepend[ Array[ Plus @@ Map[ Times @@ #1 &, FactorInteger[ # ] ] &, 100, 2 ], 0 ]; Table[sigma1[[n]] - sopfr[[n]], {n, 100}] (* Alonso del Arte, Dec 01 2004 *)

Prog

(PARI) sodf(n)=local(x); x=factor(n); sum(i=1, length(x[, 1]), sum(j=1, x[i, 2], x[i, 1])); for(i=1, 60, print1(sigma(i)-sodf(i)", "))

Crossrefs

Cf. A000203, A001414.

Sequence in context: A099749 A210442 A077202 * A273013 A050521 A266724

Adjacent sequences: A086662 A086663 A086664 * A086666 A086667 A086668

Keyword

nonn

Author

Jon Perry, Jul 27 2003

Status

approved