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Numbers k such that sequence of type a_k(n): {a(1) = 1, for n >= 2: a(n) = the smallest number h such that sigma(h) = A000203(h) = a(n-1) + k, a(n) = 0 if no such number exists} is sequence A063524(n) for n >= 1.
5

%I #10 Mar 22 2024 06:48:59

%S 9,10,16,21,22,25,26,33,34,45,46,49,50,51,52,58,64,65,66,69,70,75,76,

%T 81,82,85,86,87,88,94,99,100,105,106,115,116,117,118,122,129,130,134,

%U 135,136,141,142,145,146,147,148,153,154,165,166,169,172,177,178,184,187,188,189,190,196

%N Numbers k such that sequence of type a_k(n): {a(1) = 1, for n >= 2: a(n) = the smallest number h such that sigma(h) = A000203(h) = a(n-1) + k, a(n) = 0 if no such number exists} is sequence A063524(n) for n >= 1.

%C Sequence of composite numbers.

%C A063524(n) = characteristic function of 1 = 1,0,0,0,0,0,0,0,0,0,0,0, ...

%C Numbers k such that A051444(k) = A051444(k+1) = 0.

%C Complement of A173016.

%H Amiram Eldar, <a href="/A173015/b173015.txt">Table of n, a(n) for n = 1..10000</a>

%e a(1) = k = 9 because a_9(n) = A063524(n) = 1,0,0,0,0,0,0,0,0,0,0,0, ...

%t seq[max_] := Module[{t = Table[1, {max}]}, t[[Complement[Range[max], Table[ DivisorSigma[1, n], {n, 1, max}]]]] = 0; SequencePosition[t, {0, 0}][[;; , 1]]]; seq[200] (* _Amiram Eldar_, Mar 22 2024 *)

%Y Cf. A000035, A000203, A051444, A063524, A173012, A173013, A173014, A173016.

%K nonn

%O 1,1

%A _Jaroslav Krizek_, Nov 06 2010

%E More terms from _Amiram Eldar_, Mar 22 2024