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

Author

Juri-Stepan Gerasimov, May 29 2014

Keywords

• nonn

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

Examples

			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.
		

Links

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

Crossrefs

Cf. A005117, A048250.

Programs

Mathematica

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

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