

A277273


Numbers k such that sigma(k) = sigma(k  d(k)).


2



55, 110, 119, 188, 238, 280, 323, 352, 646, 748, 1007, 1780, 2014, 2016, 2508, 2589, 2684, 4187, 5178, 5963, 6900, 8183, 8374, 11663, 11926, 12371, 16366, 23326, 24742, 28780, 30092, 31660, 33512, 33592, 34804, 35728, 36252, 36685, 39917, 40068
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OFFSET

1,1


COMMENTS

If a(n) is odd then 2*a(n) is also in the sequence.
If p, p+2, 3p+2 and 3p+8 are primes, then (p+2)*(3p+2) is in the sequence. Dickson's conjecture implies that there are infinitely many such p. Terms of this form include 55, 119, 1007, 118007, 6120407, 8350007, 13083407, 51875207.  Robert Israel, Nov 20 2016


LINKS

Robert Israel, Table of n, a(n) for n = 1..448


EXAMPLE

A000203(55) = 72 and A000203(72  A000005(55)) = A000203(55  4) = A000203(51) = 72, therefore 55 is in the sequence.


MAPLE

select(n > numtheory:sigma(n) = numtheory:sigma(n  numtheory:tau(n)), [$2..10^5]); # Robert Israel, Nov 20 2016


MATHEMATICA

Select[Range[10^5], DivisorSigma[1, #]==DivisorSigma[1, #DivisorSigma[0, #]]&]


PROG

(PARI) isok(n) = sigma(n) == sigma(n  numdiv(n)); \\ Michel Marcus, Oct 09 2016
(MAGMA) [n: n in [3..50000]  DivisorSigma(1, n) eq DivisorSigma(1, nDivisorSigma(0, n))]; // Vincenzo Librandi, Nov 21 2016


CROSSREFS

Cf. A000005, A000203, A049820.
Sequence in context: A044525 A323070 A118151 * A275124 A282768 A217429
Adjacent sequences: A277270 A277271 A277272 * A277274 A277275 A277276


KEYWORD

easy,nonn


AUTHOR

Ivan N. Ianakiev, Oct 08 2016


STATUS

approved



