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A065300 Numbers n such that sum of divisors is a squarefree number. 5
1, 2, 4, 5, 8, 9, 13, 16, 18, 20, 25, 26, 29, 36, 37, 41, 45, 49, 50, 61, 64, 72, 73, 74, 80, 100, 101, 104, 109, 113, 116, 117, 121, 122, 128, 137, 144, 146, 148, 157, 169, 173, 180, 181, 193, 196, 200, 208, 218, 225, 229, 234, 242, 244, 256, 257, 261, 277, 281 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Numbers n such that sigma(n) divides primorial(n), that is, A002110(n) mod A000203(n) = 0. - Gary Detlefs, May 02 2012

LINKS

Harry J. Smith, Table of n, a(n) for n = 1..1000

FORMULA

Solutions to |mu(sigma(x))| = 1.

EXAMPLE

For m=100, sigma(100) = 217 = 7*31.

MATHEMATICA

Select[Range@ 300, SquareFreeQ@ DivisorSigma[1, #] &] (* or *)

Select[Range@ 300, Abs@ MoebiusMu@ DivisorSigma[1, #] == 1 &] (* Michael De Vlieger, Mar 18 2017 *)

PROG

(PARI) { n=0; for (m = 1, 10^9, if (abs(moebius(sigma(m)))==1, write("b065300.txt", n++, " ", m); if (n==1000, return)) ) } \\ Harry J. Smith, Oct 15 2009

(PARI) for(n=1, 300, if(issquarefree(sigma(n)), print1(n, ", "))) \\ Indranil Ghosh, Mar 19 2017

(Python)

from sympy import mobius, divisor_sigma

from sympy.ntheory.factor_ import core

[n for n in range(1, 301) if abs(mobius(divisor_sigma(n, 1))) == 1] #* or *#

[n for n in range(1, 301) if core(divisor_sigma(n, 1)) == divisor_sigma(n, 1)] # Indranil Ghosh, Mar 19 2017

CROSSREFS

Cf. A000203, A008683, A065299.

Sequence in context: A101881 A143989 A064573 * A080403 A280050 A271392

Adjacent sequences:  A065297 A065298 A065299 * A065301 A065302 A065303

KEYWORD

nonn

AUTHOR

Labos Elemer, Oct 29 2001

STATUS

approved

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Last modified June 6 04:15 EDT 2020. Contains 334859 sequences. (Running on oeis4.)