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.
Original entry on oeis.org
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
a(1) = k = 9 because a_9(n) = A063524(n) = 1,0,0,0,0,0,0,0,0,0,0,0, ...
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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 *)
A173016
Numbers k such that the sequence B = B_k defined by {B(1) = 1; for i >= 2: B(i) = the smallest number h such that sigma(h) = A000203(h) = B(i-1) + k; or B(i) = 0 if no such number h exists} is not the sequence {A063524(j): j >= 1}.
Original entry on oeis.org
1, 2, 3, 4, 5, 6, 7, 8, 11, 12, 13, 14, 15, 17, 18, 19, 20, 23, 24, 27, 28, 29, 30, 31, 32, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 47, 48, 53, 54, 55, 56, 57, 59, 60, 61, 62, 63, 67, 68, 71, 72, 73, 74, 77, 78, 79, 80, 83, 84, 89, 90, 91, 92, 93, 95, 96, 97, 98, 101
Offset: 1
a(1) = k = 1 because a_1(n)= A000035(n) = 1,0,1,0,1,0,1,0,1,0,1,0, ...
a(2) = k = 2 because a_2(n)= A173012(n) = 1,2,3,0,0,0,0,0,0,0,0,0, ...
a(3) = k = 3 because a_3(n)= A173013(n) = 1,3,5,7,0,2,0,2,0,2,0,2, ...
a(3) = k = 4 because a_4(n)= A173014(n) = 1,0,3,4,7,0,3,4,7,0,3,4, ...
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seq[max_] := Module[{t = Table[1, {max}]}, t[[Complement[Range[max], Table[ DivisorSigma[1, n], {n, 1, max}]]]] = 0; Complement[Range[max - 1], SequencePosition[t, {0, 0}][[;; , 1]]]]; seq[120] (* Amiram Eldar, Mar 22 2024 *)
Definition revised by Editors of OEIS, Mar 24 2024
A173012
a(1) = 1, for n >= 2; a(n) = the smallest number h such that sigma(h) = A000203(h) = a(n-1) + 2, a(n) = 0 if no such number exists.
Original entry on oeis.org
1, 2, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
Offset: 1
A173013
a(1) = 1, for n >= 2; a(n) = the smallest number h such that sigma(h) = A000203(h) = a(n-1) + 3, a(n) = 0 if no such number exists.
Original entry on oeis.org
1, 3, 5, 7, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2
Offset: 1
Showing 1-4 of 4 results.
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