A011262 In the prime factorization of n, increment odd powers and decrement even powers (multiplicative and self-inverse).

1, 4, 9, 2, 25, 36, 49, 16, 3, 100, 121, 18, 169, 196, 225, 8, 289, 12, 361, 50, 441, 484, 529, 144, 5, 676, 81, 98, 841, 900, 961, 64, 1089, 1156, 1225, 6, 1369, 1444, 1521, 400, 1681, 1764, 1849, 242, 75, 2116, 2209, 72, 7, 20, 2601, 338, 2809, 324, 3025, 784, 3249

Offset: 1

Author

Marc LeBrun

Keywords

• nonn
• easy
• mult

Links

• Paul Tek, Table of n, a(n) for n = 1..10000
• Index entries for sequences that are permutations of the natural numbers.

Crossrefs

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

Programs

Haskell

a011262 n = product $ zipWith (^)
                      (a027748_row n) (map a103889 $ a124010_row n)
-- Reinhard Zumkeller, Jun 23 2013

Mathematica

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

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

Formula

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

a(n) = Product_{k = 1..A001221(n)} A027748(n,k) ^ A103889(A124010(n,k)). - Reinhard Zumkeller, Jun 23 2013

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