A295417 Self-inverse permutation of natural numbers: in prime factorization of n replace each positive prime exponent e with max + min - e, where max = A051903(n) and min = A051904(n).

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 18, 13, 14, 15, 16, 17, 12, 19, 50, 21, 22, 23, 54, 25, 26, 27, 98, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 250, 41, 42, 43, 242, 75, 46, 47, 162, 49, 20, 51, 338, 53, 24, 55, 686, 57, 58, 59, 450, 61, 62, 147, 64, 65, 66

Offset

1,2

Comments

This sequence was inspired by A293448.

This sequence first differs from A293448 at n = 42: a(42) = 42 whereas A293448(42) = 70.

a(A293448(n)) = A293448(a(n)) for any n > 0.

a(n) = n iff n belongs to A072774.

f(n) = f(a(n)) for any n > 0 and f in { A001221, A006530, A007947, A020639, A051903, A051904 }.

The lines visible in the logarithmic scatterplot of the sequence seems to correspond to integer sets where the function A062760 is constant (see logarithmic scatterplot in Links section).

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, Colored logarithmic scatterplot of the first 1000000 terms (where the color is function of A062760(n))

Index entries for sequences that are permutations of the natural numbers

Formula

a(n) = A007947(n)^(A051903(n) + A051904(n)) / n.

Example

For n = 1620:
- 1620 = 2^2 * 3^4 * 5,
- A051903(1620) = 4 and A051904(1620) = 1,
- a(1620) = 2^(4+1-2) * 3^(4+1-4) * 5^(4+1-1) = 2^3 * 3 * 5^4 = 15000.

Prog

(PARI) a(n) = { my(f=factor(n)); if(#f~<=1, return(n), my(mi=vecmin(f[, 2]), ma=vecmax(f[, 2])); return(prod(i=1, #f~, f[i, 1]^(ma+mi-f[i, 2])))) }

Crossrefs

Cf. A001221, A006530, A007947, A020639, A051903, A051904, A062760, A072774 (fixed points), A293448.

Sequence in context: A105119 A069799 A225891 * A293448 A085079 A289234

Adjacent sequences: A295414 A295415 A295416 * A295418 A295419 A295420

Keyword

nonn

Author

Rémy Sigrist, Nov 22 2017

Status

approved