OFFSET
1,2
COMMENTS
Reverse the prime-indices in such a way that the smallest and the greatest prime dividing n (A020639 and A006530) are preserved.
a(n) = n iff n belongs to A236510. - Rémy Sigrist, Nov 22 2017
LINKS
FORMULA
EXAMPLE
For n = 25 = 5^2 = prime(3)^2, thus min = max = 3, and we form a product prime(3+(3-3))^2, thus a(25) = prime(3)^2 = 25.
For n = 42 = 2*3*7 = prime(1)*prime(2)*prime(4), thus min = 1 and max = 4, so we form a product prime(1+(4-1))*prime(1+(4-2))*prime(1+(4-4)), thus a(42) = prime(4)*prime(3)*prime(1) = 7*5*2 = 70.
For n = 126 = 2 * 3^2 * 7 = prime(1) * prime(2)^2 * prime(4), thus min = 1 and max = 4, so we form a product prime(1+(4-1)) * prime(1+(4-2))^2 * prime(1+(4-4)), thus a(126) = prime(4) * prime(3)^2 * prime(1) = 7 * 5^2 * 2 = 350.
PROG
(PARI) A293448(n) = { if(1==n, return(n)); my(f=factor(n), mini = primepi(f[1, 1]), maxi = primepi(f[#f~, 1])); for(i=1, #f~, f[i, 1] = prime((maxi-primepi(f[i, 1]))+mini)); factorback(f); }
CROSSREFS
Differs from A069799 (and some other related permutations) for the first time at n=42.
KEYWORD
nonn
AUTHOR
Antti Karttunen, Nov 09 2017
STATUS
approved