A063948 -id:A063948 - cp's OEIS frontend

A291109 Numbers that are not the sum of the squarefree divisors of some natural number.

2, 5, 7, 9, 10, 11, 13, 15, 16, 17, 19, 21, 22, 23, 25, 26, 27, 28, 29, 31, 33, 34, 35, 37, 39, 40, 41, 43, 45, 46, 47, 49, 50, 51, 52, 53, 55, 57, 58, 59, 61, 63, 64, 65, 66, 67, 69, 70, 71, 73, 75, 76, 77, 78, 79, 81, 82, 83, 85, 86, 87, 88, 89, 91, 92, 93, 94, 95, 97, 99, 100, 101, 103, 105, 106, 107, 109, 111

Offset: 1

Ilya Gutkovskiy, Aug 17 2017

nonn

Impossible values for A048250 (numbers k in increasing order such that A048250(m) = k has no solution).
Numbers that are not of the form Product (p_i + 1), p is a prime, so all odd numbers (except 1 and 3) are in this sequence.
Also numbers that are not the sum of the divisors of some squarefree number.

Robert Israel, Table of n, a(n) for n = 1..10000
Index entries for sequences related to sums of divisors

Cf. A005114, A005117, A007369, A048250, A048995, A062822, A063948, A064000, A203444, A206778, A274793.

sort(convert({$1..1000} minus map(numtheory:-sigma, select(numtheory:-issqrfree, {$1..1000})),list)); # Robert Israel, Jun 26 2018

TakeWhile[Complement[Range@ #, Union@ Table[Total@ Select[Divisors@ n, SquareFreeQ], {n, 2 #}]], Function[k, k <= #]] &@ 111

A290240 The number of unitary untouchable numbers <= 10^n.

Original entry on oeis.org

5, 5, 9, 75, 862, 9903, 101030, 1028263

Offset: 1

Amiram Eldar, Jul 24 2017

The unitary version of A057978. a(5)-a(8) were taken from the paper by Pomerance and Yang.

Carl Pomerance and Hee-Sung Yang, Variant of a theorem of Erdős on the sum-of-proper-divisors function, Mathematics of Computation, Vol. 83, No. 288 (2014), pp. 1903-1913.

Cf. A057978, A063948.

A325202 Number of times that A325177(n) occurs in the sum of proper unitary divisors function (A034460).

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 21, 24, 26, 28, 31, 33, 35, 37, 38, 45, 49, 56, 60, 63, 64, 65, 72, 73, 81, 83, 94, 100, 105, 121, 138, 145, 149, 169, 175, 176, 180, 182, 202, 210, 234, 236, 256, 285, 288, 306, 319, 343, 347, 362, 382

Offset: 1

Amiram Eldar, Sep 05 2019

nonn

The unitary version of A238896.

Cf. A034448, A034460, A063948, A238896, A324938, A325177.

us[1] = 0; us[n_] := Times @@ (1 + Power @@@ FactorInteger[n]) - n;  m = 300; v = Table[0, {m}]; Do[u = us[k]; If[2 <= u <= m, v[[u]]++], {k, 1, m^2}]; s = {}; vm = -1; Do[If[v[[k]] > vm, vm = v[[k]]; AppendTo[s, vm]], {k, 2, m}]; s

a(n) = A324938(A325177(n)).

cp's OEIS Frontend

A291109 Numbers that are not the sum of the squarefree divisors of some natural number.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

Mathematica

A290240 The number of unitary untouchable numbers <= 10^n.

Views

Author

Keywords

Comments

Links

Crossrefs

A325202 Number of times that A325177(n) occurs in the sum of proper unitary divisors function (A034460).

Views

Author

Keywords

Comments

Crossrefs

Programs

Mathematica

Formula