A368825 -id:A368825 - cp's OEIS frontend

A368827 Indices k where A368825(k) = 1.

1, 15, 19, 22, 24, 51, 57, 66, 86, 89, 122, 127, 134, 179, 183, 224, 265, 287, 288, 326, 368, 402, 425, 455, 458, 461, 530, 535, 650, 668, 674, 675, 687, 803, 825, 854, 890, 897, 953, 997, 1147, 1261, 1341, 1371, 1381, 1442, 1443, 1466, 1475, 1587, 1650, 1662, 1691, 1734, 1743, 1755, 1965

Offset: 1

Scott R. Shannon, Jan 07 2024

nonn

There are 2095 indices less than 2 million. In this range on fifteen occasions the indices are consecutive - these indices begin 287, 288, 674, 675, 1442, 1443, 3362, 3363, ... .

Scott R. Shannon, Table of n, a(n) for n = 1..2095

Cf. A368825, A368823, A055231, A005117, A124010.

A368823 a(1) = 1; for n > 1, a(n) = A055231(a(n-1) * n), where A055231(k) is the powerfree part of k.

Original entry on oeis.org

1, 2, 6, 3, 15, 10, 70, 35, 35, 14, 154, 231, 3003, 858, 1430, 715, 12155, 24310, 461890, 46189, 969969, 176358, 4056234, 676039, 676039, 104006, 104006, 7429, 215441, 6463230, 200360130, 100180065, 367326905, 43214930, 60500902, 30250451, 1119266687, 117817546, 4594884294, 11487210735

Offset: 1

Scott R. Shannon, Jan 07 2024

nonn

Terms are squarefree. - Michael De Vlieger, Jan 07 2024.

			a(4) = 3 as a(3)*4 = 6*4 = 24 = 2*2*2*3, and the powerfree part of 24 is 3.

Cf. A368825 (addition), A055231, A005117, A124010.

f[x_] := Times @@ Map[#1^(#2 Boole[#2 == 1]) & @@ # &, FactorInteger[x]]; a[n_] := f[n* a[n - 1]]; a[1] = 1; Array[a, 120] (* Michael De Vlieger, Jan 07 2024 *)

cp's OEIS Frontend

A368827 Indices k where A368825(k) = 1.

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A368823 a(1) = 1; for n > 1, a(n) = A055231(a(n-1) * n), where A055231(k) is the powerfree part of k.

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