A206029 a(n) = sum of numbers k <= sigma(n) such that k is not equal to sigma(d) for any divisor d of n where sigma = A000203.

0, 2, 5, 17, 14, 58, 27, 94, 73, 143, 65, 351, 90, 264, 265, 439, 152, 708, 189, 826, 483, 614, 275, 1700, 458, 843, 762, 1497, 434, 2488, 495, 1896, 1111, 1409, 1113, 3988, 702, 1746, 1521, 3913, 860, 4476, 945, 3427, 2955, 2528, 1127, 7465, 1587, 4219

Offset

1,2

Comments

In sequence A007429 are added all values of sigma(d) of all divisors d of numbers n, in sequence A206028 are added only distinct values of sigma(d) of all divisors d of numbers n and in sequence a(n) are added numbers k (1<=k<=sigma(n)) such that sigma(d) = k has no solution for neither divisor d of number n.

Links

Table of n, a(n) for n=1..50.

Formula

a(n) = A184387(n) - A206028 = A000217(A000203(n)) - A206028.

Example

For n=6 -> divisors d of 6: 1,2,3,6; corresponding values of sigma(d): 1,3,4,12; a(6) = Sum of k = 2+5+6+7+8+9+10+11 = 58.

Mathematica

Table[Total[Complement[Range[DivisorSigma[1, n]], DivisorSigma[1, Divisors[n]]]], {n, 100}] (* T. D. Noe, Feb 10 2012 *)

Crossrefs

Cf. A000203, A206030, A007429, A206028.

Sequence in context: A005529 A259255 A274903 * A057282 A276767 A123364

Adjacent sequences: A206026 A206027 A206028 * A206030 A206031 A206032

Keyword

nonn

Author

Jaroslav Krizek, Feb 03 2012

Status

approved