A063466 Numbers k such that 2*phi(k) + 8 = sigma(k).

6, 15, 21, 33, 39, 51, 57, 69, 87, 93, 111, 123, 129, 141, 159, 175, 177, 183, 201, 213, 219, 237, 249, 267, 291, 303, 309, 321, 327, 339, 381, 393, 411, 417, 447, 453, 471, 489, 501, 519, 537, 543, 573, 579, 591, 597, 633, 669, 681, 687, 699, 717, 723, 753

Offset

1,1

Comments

For 16 < n < 10^8, a(n) = 3*prime(n). Note also that a(n) is odd for n > 1. - Charles R Greathouse IV, Nov 19 2015

Links

Harry J. Smith, Table of n, a(n) for n = 1..10000

Example

If p is a prime other than 3, 2*phi(3p) = 2(2p-2) = 4p - 4, sigma(3p) = 4p + 4, 2*phi(3p) + 8 = sigma(3p). So numbers of the form 3p are in the sequence. Also if k=175, phi(175) = 120, sigma(175) = 248, thus 2*phi(175) + 8 = sigma(175), so 175 is here. Note that 175 is not of the form 3p. No additional terms not of the form 3p were found below 100000.

Mathematica

Select[Range[800], 2*EulerPhi[#]+8==DivisorSigma[1, #]&] (* Harvey P. Dale, Dec 28 2017 *)

Prog

(PARI) n=-1; for (m=1, 10^9, if (sigma(m) - 2*eulerphi(m) == 8, write("b063466.txt", n++, " ", m); if (n==1000, break))) \\ Harry J. Smith, Aug 22 2009
(PARI) is(n)=my(f=factor(n)); 2*eulerphi(f)+8 == sigma(f) \\ Charles R Greathouse IV, Nov 19 2015

Crossrefs

Cf. A000010, A000203.

Sequence in context: A015793 A373899 A261078 * A377713 A138109 A377792

Adjacent sequences: A063463 A063464 A063465 * A063467 A063468 A063469

Keyword

nonn

Author

Labos Elemer, Jul 26 2001

Status

approved