A095380 Number of integers not exceeding 2^n that are impossible as sum-of-divisors of other numbers.

1, 1, 2, 6, 15, 34, 75, 162, 337, 706, 1466, 2995, 6119, 12450, 25248, 51158, 103450, 209010, 421681, 850322, 1712673, 3447970, 6937759, 13952296, 28049834, 56369395, 113241087, 227428919, 456641954, 916642515, 1839651364, 3691364919, 7405635242

Offset

1,3

Comments

Conjecture: ratio of non-sigma numbers tends to one. Increasing majority of numbers is impossible as a sum of divisors.

Links

Table of n, a(n) for n=1..33.

Formula

a(n) is the number of terms in A007369 not exceeding 2^n.

Example

n=5: {2,5,9,10,11,16,17,19,21,22,23,25,26,27,29} are the 15 terms <= 2^5 in A007369.

Mathematica

Table[a = {}; Do[s = DivisorSigma[1, n]; a = Append[a, s], {n, 1, 2^j} ]; Length[ Complement[ Table[ n, {n, 1, 2^j} ], Union[a] ] ], {j, 12}]

Crossrefs

Cf. A007369.

Sequence in context: A192980 A281970 A221719 * A287012 A355061 A336957

Adjacent sequences: A095377 A095378 A095379 * A095381 A095382 A095383

Keyword

nonn

Author

Labos Elemer and Antti Karttunen, Jun 07 2004

Extensions

a(19)-a(31) from Donovan Johnson, Nov 30 2008

a(32)-a(33) from Donovan Johnson, Aug 06 2011

Status

approved