A173015 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.

9, 10, 16, 21, 22, 25, 26, 33, 34, 45, 46, 49, 50, 51, 52, 58, 64, 65, 66, 69, 70, 75, 76, 81, 82, 85, 86, 87, 88, 94, 99, 100, 105, 106, 115, 116, 117, 118, 122, 129, 130, 134, 135, 136, 141, 142, 145, 146, 147, 148, 153, 154, 165, 166, 169, 172, 177, 178, 184, 187, 188, 189, 190, 196

Offset

1,1

Comments

Sequence of composite numbers.

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

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

Complement of A173016.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

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

Mathematica

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 *)

Crossrefs

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

Sequence in context: A280846 A121061 A106690 * A045568 A191380 A088036

Adjacent sequences: A173012 A173013 A173014 * A173016 A173017 A173018

Keyword

nonn

Author

Jaroslav Krizek, Nov 06 2010

Extensions

More terms from Amiram Eldar, Mar 22 2024

Status

approved