%I #23 Sep 08 2022 08:46:17

%S 55,110,119,188,238,280,323,352,646,748,1007,1780,2014,2016,2508,2589,

%T 2684,4187,5178,5963,6900,8183,8374,11663,11926,12371,16366,23326,

%U 24742,28780,30092,31660,33512,33592,34804,35728,36252,36685,39917,40068

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

%C If a(n) is odd then 2*a(n) is also in the sequence.

%C 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

%H Robert Israel, <a href="/A277273/b277273.txt">Table of n, a(n) for n = 1..448</a>

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

%p select(n -> numtheory:-sigma(n) = numtheory:-sigma(n - numtheory:-tau(n)), [$2..10^5]); # _Robert Israel_, Nov 20 2016

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

%o (PARI) isok(n) = sigma(n) == sigma(n - numdiv(n)); \\ _Michel Marcus_, Oct 09 2016

%o (Magma) [n: n in [3..50000] | DivisorSigma(1, n) eq DivisorSigma(1, n-DivisorSigma(0, n))]; // _Vincenzo Librandi_, Nov 21 2016

%Y Cf. A000005, A000203, A049820.

%K easy,nonn

%O 1,1

%A _Ivan N. Ianakiev_, Oct 08 2016