

A243128


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


1



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
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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: A074214 A036897 A129966 * A306771 A216521 A110172
Adjacent sequences: A243125 A243126 A243127 * A243129 A243130 A243131


KEYWORD

nonn


AUTHOR

JuriStepan Gerasimov, May 29 2014


STATUS

approved



