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In the prime factorization of n, increment odd powers and decrement even powers (multiplicative and self-inverse).
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%I #24 Oct 13 2022 05:57:41

%S 1,4,9,2,25,36,49,16,3,100,121,18,169,196,225,8,289,12,361,50,441,484,

%T 529,144,5,676,81,98,841,900,961,64,1089,1156,1225,6,1369,1444,1521,

%U 400,1681,1764,1849,242,75,2116,2209,72,7,20,2601,338,2809,324,3025,784,3249

%N In the prime factorization of n, increment odd powers and decrement even powers (multiplicative and self-inverse).

%H Paul Tek, <a href="/A011262/b011262.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>.

%F Multiplicative with f(p^k) = p^(k-1) if k even, p^(k+1) if k odd.

%F a(n) = Product_{k = 1..A001221(n)} (A027748(n,k) ^ A103889(A124010(n,k)). - _Reinhard Zumkeller_, Jun 23 2013

%F Sum_{k=1..n} a(k) ~ c * n^3, where c = (1/3) * Product_{p prime} ((p^5 + p^4 - p + 1)/(p^5 + p^4 + p^3 + p^2)) = 0.21311151701724196530... . - _Amiram Eldar_, Oct 13 2022

%t f[n_, k_] := n^(If[EvenQ[k], k - 1, k + 1]); Table[Times @@ f @@@ FactorInteger[n], {n, 57}] (* _Jayanta Basu_, Aug 14 2013 *)

%o (PARI) a(n)=my(f=factor(n));return(prod(i=1,#f[,1],f[i,1]^(f[i,2]-(-1)^f[i,2]))) \\ _Paul Tek_, Jun 01 2013

%o (Haskell)

%o a011262 n = product $ zipWith (^)

%o (a027748_row n) (map a103889 $ a124010_row n)

%o -- _Reinhard Zumkeller_, Jun 23 2013

%Y Cf. A001221, A011264, A027748, A103889, A124010.

%K nonn,easy,mult

%O 1,2

%A _Marc LeBrun_