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A201880 Numbers n such that sigma_2(n) - n^2 is prime. 0
4, 18, 21, 33, 39, 72, 93, 99, 100, 159, 171, 177, 189, 207, 213, 231, 245, 249, 261, 275, 291, 297, 303, 333, 338, 357, 369, 381, 399, 400, 453, 471, 475, 477, 484, 495, 537, 539, 543, 561, 609, 633, 648, 657, 669, 681, 711, 717, 783, 801, 833, 861, 909, 927 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Numbers n such that sum of the square of proper (or aliquot) divisors of n is a prime number.

LINKS

Table of n, a(n) for n=1..54.

FORMULA

{n: A067558(n) in A000040} - R. J. Mathar, Dec 07 2011

EXAMPLE

a(3)=21 because the aliquot divisors of 21 are 1, 3, 7, the sum of whose squares is 1^2 + 3^2 + 7^2 = 59, prime.

MAPLE

A067558 := proc(n)

    numtheory[sigma][2](n)-n^2 ;

end proc:

isA201880 := proc(n)

    isprime(A067558(n)) ;

end proc:

for n from 1 to 1000 do

    if isA201880(n) then

        printf("%d, ", n);

    end if;

end do: # R. J. Mathar, Dec 07 2011

MATHEMATICA

Select[Range[400], PrimeQ[DivisorSigma[2, #]-#^2]&]

PROG

(PARI) is(n)=isprime(sigma(n, 2)-n^2) \\ Charles R Greathouse IV, Dec 06 2011

CROSSREFS

Cf. A037020.

Sequence in context: A045019 A103061 A230605 * A022384 A093022 A255409

Adjacent sequences:  A201877 A201878 A201879 * A201881 A201882 A201883

KEYWORD

nonn

AUTHOR

Michel Lagneau, Dec 06 2011

STATUS

approved

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Last modified May 26 18:04 EDT 2019. Contains 323597 sequences. (Running on oeis4.)