A349983 -id:A349983 - cp's OEIS frontend

A350723 Integer defect of n: a(n) = A005245(n) - A349983(n).

0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 2, 0, 1, 1, 1, 1, 2, 0, 1, 1, 1, 2, 3, 1, 2, 2, 0, 1, 2, 1, 2, 1, 2, 2, 2, 0, 1, 1, 1, 1, 2, 1, 2, 2, 1, 2, 3, 1, 2, 2, 2, 2, 3, 0, 1, 1, 1, 2, 3, 1, 2, 2, 1, 1, 2, 2, 3, 2, 3, 2, 3, 1

Offset: 1

Harry Altman, Feb 06 2022

nonn

Harry Altman, Integer Complexity: The Integer Defect, Moscow Journal of Combinatorics and Number Theory 8-3 (2019), 193-217.

Harry Altman, Integer Complexity: The Integer Defect, arXiv:1804.07446 [math.NT], 2018.

Difference between A005245 and A349983 (the latter being almost the same as A007600).

A351467 Numbers with integer defect at most 1; m such that A350723(m) <= 1.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 18, 19, 20, 21, 24, 27, 28, 30, 32, 36, 37, 38, 39, 40, 42, 45, 48, 54, 55, 56, 57, 60, 63, 64, 72, 81, 82, 84, 90, 96, 108, 109, 110, 111, 112, 114, 117, 120, 126, 128, 135, 144, 162, 163, 164, 165, 168, 171

Offset: 1

Harry Altman, Feb 12 2022

m appears in this list if and only if it can be written as 2^p*3^r for p <= 10 or as 2^p*(2^q*3^r+1)*3^s for p+q <= 2.

Harry Altman, Integer Complexity: The Integer Defect, Moscow Journal of Combinatorics and Number Theory 8-3 (2019), 193-217.

Harry Altman, Integer Complexity: The Integer Defect, arXiv:1804.07446 [math.NT], 2018.

Cf. A350723, A005245, A349983. Contains A000792 as a subset.

cp's OEIS Frontend

A350723 Integer defect of n: a(n) = A005245(n) - A349983(n).

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