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A191218 Odd numbers n such that sigma(n) is congruent to 2 modulo 4. 8
5, 13, 17, 29, 37, 41, 45, 53, 61, 73, 89, 97, 101, 109, 113, 117, 137, 149, 153, 157, 173, 181, 193, 197, 229, 233, 241, 245, 257, 261, 269, 277, 281, 293, 313, 317, 325, 333, 337, 349, 353, 369, 373, 389, 397, 401, 405, 409, 421, 425, 433, 449, 457, 461, 477 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Exactly the numbers of the form p^{4k+1}*m^2 with p a prime congruent to 1 modulo 4 and m a positive integer coprime with p. The odd perfect numbers are all of this form.

See A228058 for the terms where m > 1. - Antti Karttunen, Apr 22 2019

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..20000

Index entries for sequences related to sigma(n)

EXAMPLE

For n=3 one has a(3)=17 since sigma(17) = 18 = 4*4 +2 is congruent to 2 modulo 4

MAPLE

with(numtheory): genodd := proc(b) local n, s, d; for n from 1 to b by 2 do s := sigma(n);

if modp(s, 4)=2 then print(n); fi; od; end;

MATHEMATICA

Select[Range[1, 501, 2], Mod[DivisorSigma[1, #], 4]==2&] (* Harvey P. Dale, Nov 12 2017 *)

PROG

(PARI) forstep(n=1, 10^3, 2, if(2==(sigma(n)%4), print1(n, ", "))) \\ Joerg Arndt, May 27 2011

(PARI) list(lim)=my(field=vectorsmall(lim\=1), v=List(), x2, t); for(x=2, sqrtint(lim-1), x2=x^2; t=sqrtint(lim-x2); forstep(y=if(t<x, t-(x-t+1)%2, x-1), 1, -2, field[x2+y^2]++)); forstep(n=3, sqrtint(lim), 2, field[n^2]=0); for(n=2, lim, if(field[n]==1, listput(v, n))); field=0; Vec(v) \\ Charles R Greathouse IV, Jan 06 2018

CROSSREFS

Subsequence of A191217.

Cf. A228058, A324898 (subsequences).

Cf. A000203, A191219, A324647, A324718, A324719.

Sequence in context: A113482 A208853 A265889 * A279857 A077426 A231754

Adjacent sequences:  A191215 A191216 A191217 * A191219 A191220 A191221

KEYWORD

nonn,easy

AUTHOR

Luis H. Gallardo, May 26 2011

STATUS

approved

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Last modified August 19 08:26 EDT 2019. Contains 326115 sequences. (Running on oeis4.)