A361809 -id:A361809 - cp's OEIS frontend

A181820 a(1) = 1; for n > 1, if A025487(n) = Product p(i)^e(i), then a(n) = Product p(e(i)).

1, 2, 3, 4, 5, 6, 7, 10, 8, 11, 9, 14, 12, 13, 15, 22, 20, 17, 21, 18, 26, 16, 25, 28, 19, 33, 30, 34, 24, 35, 44, 23, 39, 42, 38, 40, 55, 27, 52, 29, 50, 51, 36, 49, 66, 46, 56, 65, 45, 68, 31, 70, 57, 32, 60, 77, 78, 58, 88, 85, 63, 76, 37, 110, 69, 48, 84, 91, 75, 102, 62, 54, 98, 104, 95

Offset: 1

Matthew Vandermast, Dec 07 2010

nonn

A permutation of the positive integers.

The partition given by the prime signature of A025487(n) has Heinz number a(n). - Pontus von Brömssen, Mar 25 2023

			A025487(8) = 24 = 2^3*3 has the exponents (3,1) in its canonical prime factorization. Accordingly, a(8) = prime(3)*prime(1) (i.e., A000040(3)*A000040(1)), which equals 5*2=10.

A181815 is another mapping from the members of A025487 to the positive integers. Also see A181819, A181821.

Cf. A000040, A122111, A361808 (inverse), A361809 (fixed points).

a(n) = A181819(A025487(n)).

a(n) = A122111(A181815(n)).

A361808 Inverse permutation to A181820.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 9, 11, 8, 10, 13, 14, 12, 15, 22, 18, 20, 25, 17, 19, 16, 32, 29, 23, 21, 38, 24, 40, 27, 51, 54, 26, 28, 30, 43, 63, 35, 33, 36, 80, 34, 98, 31, 49, 46, 119, 66, 44, 41, 42, 39, 145, 72, 37, 47, 53, 58, 173, 55, 207, 71, 61, 114, 48, 45

Offset: 1

Pontus von Brömssen, Mar 25 2023

nonn

The partition with Heinz number n is given by the prime signature of A025487(a(n)).

			The partition with Heinz number 18 = prime(1)^1*prime(2)^2 is (1,2,2), and prime(1)^2*prime(2)^2*prime(3)^1 = 180 = A025487(20), so a(18) = 20.

Index entries for sequences that are permutations of the positive integers

Cf. A025487, A181820, A361809 (fixed points).

a(A181820(n)) = A181820(a(n)) = n.

cp's OEIS Frontend

A181820 a(1) = 1; for n > 1, if A025487(n) = Product p(i)^e(i), then a(n) = Product p(e(i)).

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