A036898 -id:A036898 - cp's OEIS frontend

A360779 Refactorable numbers gaps: differences between consecutive refactorable numbers.

1, 6, 1, 3, 6, 6, 12, 4, 16, 4, 12, 8, 4, 4, 8, 8, 4, 20, 4, 4, 16, 4, 24, 4, 20, 21, 3, 4, 8, 8, 4, 24, 12, 8, 32, 16, 4, 12, 12, 4, 8, 12, 28, 17, 3, 4, 2, 18, 4, 8, 8, 4, 12, 12, 20, 24, 4, 4, 16, 16, 12, 13, 7, 4, 4, 24, 8, 12, 24, 4, 8, 12, 44, 16, 12, 4, 16, 4, 24

Offset: 1

Ctibor O. Zizka, Feb 20 2023

nonn

Empirically it looks as though the consecutive refactorable numbers >= 8 with odd gaps between them always occur in triples: [8, 9, 12], [204, 225, 228], [424, 441, 444], [612, 625, 632], [1068, 1089, 1096], [1520, 1521, 1524], and so on. The sum of the gaps in the triple is divisible by 4. The middle term of a triple is an odd refactorable number, see A036896.

			a(1) = 2 - 1 = 1;
a(2) = 8 - 2 = 6;
a(3) = 9 - 8 = 1;
and so on.

Cf. A033950, A036896, A036898, A114617.

Differences[Select[Range[1000], Divisible[#, DivisorSigma[0, #]] &]] (* Amiram Eldar, Feb 20 2023 *)

lista(nn) = my(v=select(x->!(x % numdiv(x)), [1..nn])); vector(#v-1, k, v[k+1]-v[k]); \\ Michel Marcus, Feb 20 2023

a(n) = A033950(n + 1) - A033950(n).

cp's OEIS Frontend

A360779 Refactorable numbers gaps: differences between consecutive refactorable numbers.

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