A292762 Numbers of the form p^k or 2*p^k, where p is a prime == 3 mod 4 and k is odd.

3, 6, 7, 11, 14, 19, 22, 23, 27, 31, 38, 43, 46, 47, 54, 59, 62, 67, 71, 79, 83, 86, 94, 103, 107, 118, 127, 131, 134, 139, 142, 151, 158, 163, 166, 167, 179, 191, 199, 206, 211, 214, 223, 227, 239, 243, 251, 254, 262, 263, 271, 278, 283, 302, 307, 311, 326, 331, 334, 343, 347, 358, 359, 367, 379, 382

Offset

1,1

Comments

Numbers m such that sigma(m) == 0 mod 4 and phi(m) == 2 mod 4.

Links

David A. Corneth, Table of n, a(n) for n = 1..13839 (Terms up to 200000)

Formula

As 22 = 2 * 11^1, which is of the form 2 * p^k with p = 11 = 2 * 4 + 3 == 3 mod 4 and k = 1 which is odd, 22 is a term. - David A. Corneth, Oct 02 2017

Mathematica

Do[If[Mod[DivisorSigma[1, n], 4]==0 && Mod[EulerPhi[n], 4]==2, Print[n]], {n, 1, 10^3}] (* Vincenzo Librandi, Oct 02 2017 *)

Prog

(PARI) isok(m) = ((sigma(m) % 4) == 0) && ((eulerphi(m) % 4) == 2); \\ Michel Marcus, Oct 02 2017
(PARI) upto(n) = {my(l=List()); forprime(p=3, n, if(p%4==3, forstep(e=1, logint(n, p), 2, listput(l, p^e); if(2*p^e <= n, listput(l, 2*p^e))))); listsort(l); l} \\ David A. Corneth, Oct 02 2017

Crossrefs

Intersection of A097987 and A248150.

Cf. A000010, A000203.

Sequence in context: A126003 A047556 A255053 * A374845 A364927 A258233

Adjacent sequences: A292759 A292760 A292761 * A292763 A292764 A292765

Keyword

nonn

Author

N. J. A. Sloane, Sep 26 2017

Status

approved