A277273 - OEIS

A277273

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

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, n-DivisorSigma(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