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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
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).
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
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Nov 22 2017
STATUS
approved