A243128 Squarefree numbers k such that 4k <= sum of squarefree divisors of 4k.

3, 15, 21, 33, 35, 39, 51, 57, 69, 87, 93, 105, 111, 123, 129, 141, 159, 165, 177, 183, 195, 201, 213, 219, 231, 237, 249, 255, 267, 273, 285, 291, 303, 309, 321, 327, 339, 345, 357, 381, 385, 393, 399, 411, 417, 429, 435, 447, 453

Offset

1,1

Comments

Odd squarefree numbers n such that sigma(n)/n >= 4/3. - Charles R Greathouse IV, May 30 2014

Includes all odd squarefree multiples of its terms. The primitive members are 3, 35, 715, 935, 1001, 1045, 1105, 1235, 1265, .... - Charles R Greathouse IV, May 30 2014

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Example

3 is in this sequence because 3 is squarefree and 4*3 = A048250(4*3) = 12;
21 is in this sequence because 21 is squarefree and 4*21 = 84 < A048250(4*21) = 96.

Mathematica

Select[2Range[250] + 1, MoebiusMu[#] != 0 && DivisorSigma[1, #]/# >= 4/3 &] (* Alonso del Arte, May 31 2014 *)

Prog

(PARI) isok(n) = issquarefree(n) && (sumdiv(4*n, d, issquarefree(d)*d) >= 4*n); \\ Michel Marcus, May 30 2014
(PARI) is(n)=my(f=factor(n)); n%2 && n>1 && vecmax(f[, 2])==1 && sigma(f, -1) >= 4/3 \\ Charles R Greathouse IV, May 30 2014

Crossrefs

Cf. A005117, A048250.

Sequence in context: A036897 A129966 A354675 * A306771 A216521 A110172

Adjacent sequences: A243125 A243126 A243127 * A243129 A243130 A243131

Keyword

nonn

Author

Juri-Stepan Gerasimov, May 29 2014

Status

approved