A317101 Numbers whose prime multiplicities are pairwise indivisible.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 21, 22, 23, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 46, 47, 49, 51, 53, 55, 57, 58, 59, 61, 62, 64, 65, 66, 67, 69, 70, 71, 72, 73, 74, 77, 78, 79, 81, 82, 83, 85, 86, 87

Offset

1,2

Comments

From Michael De Vlieger, Mar 06 2026: (Start)

Does not intersect A332785 (numbers that are neither squarefree nor powerful) since there exists an exponent 1 amid the prime power factor exponents, there exist at least 2 distinct exponents, and 1 divides all other numbers.

Does not intersect A386762 (perfect powers of numbers in A332785).

Does not intersect A390055, union of A332785 and A386762.

Both A303554 (union of squarefree numbers A005117 and prime powers A000961) and A303606 are proper subsets, therefore A072774 is a proper subset.

Does not contain certain Achilles numbers with more than 2 distinct prime factors, where there exists at least one pair of prime power factor exponents {k,m} such that k | m. Example, 10800 = 2^4 * 3^3 * 5^2; 2 | 4, therefore 10800 is not in this sequence. (End)

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Example

72 = 2^3 * 3^2 is in the sequence because 3 and 2 are pairwise indivisible.
144 = 2^4*3^2 is not in the sequence because 4 is divisible by 2. - R. J. Mathar, Mar 06 2026

Mathematica

Select[Range[100], Select[Tuples[Last/@FactorInteger[#], 2], And[UnsameQ@@#, Divisible@@#]&]=={}&]

Crossrefs

Cf. A052486, A072774, A118914, A124010, A285572, A285573, A303362, A303606, A304713, A316475, A317102, A317616, A332785, A386762, A390055.

Sequence in context: A283550 A271113 A325369 * A393924 A304449 A085924

Adjacent sequences: A317098 A317099 A317100 * A317102 A317103 A317104

Keyword

nonn

Author

Gus Wiseman, Aug 01 2018

Status

approved