1,1

A permutation ofA028983.

A007417(which has asymptotic density 3/4) lists index n such that a(n) = 3n. The sequence maps the terms ofA0074171:1 ontoA145204\{0}, defining a bijection between them.

Similarly, bijections are defined from the odd numbers (A005408) to the nonsquare odd numbers (A088828), from the positive even numbers (A299174) toA088829,fromA003159to the nonsquares inA003159,and fromA325424to the nonsquares inA036668.The latter two bijections are between sets where membership depends on whether a number's squarefree part divides by 2 and/or 3.

a(n) = n * p / (A034386(p-1)/2), where p =A284723(A007913(n)).

a(n) =A334747(A334747(n)).

a(n) =A331590(3, n) =A225546(4 *A225546(n)).

a(2*n) = 2 * a(n).

a(A019565(n)) =A019565(n+2).

a(k * m^2) = a(k) * m^2.

a(A003961(n)) =A003961(A334747(n)).

a(A070826(n)) = prime(n+1).

A048675(a(n)) =A048675(n) + 2.

A008833(a(n)) =A008833(n).

A267116(a(n)) =A267116(n) OR 1, where OR denotes the bitwise operationA003986.

a(A007417(n)) =A145204(n+1) = 3 *A007417(n).

84 = 21*4 has squarefree part 21 (and square part 4). The smallest odd prime absent from 21 = 3*7 is 5 and the product of all smaller odd primes is 3. So a(84) = 84*5/3 = 140.

(PARI) a(n) = {my(c=core(n), m=n); forprime(p=3,, if(c % p, m*=p; break, m/=p)); m; } \\Michel Marcus,May 22 2020

Permutation ofA028983.

Row 3, and therefore column 3, ofA331590.Cf.A334747(row 2).

A007913,A034386,A225546,A284723are used in formulas defining the sequence.

The formula section details how the sequence maps the terms ofA003961,A019565,A070826;and how f(a(n)) relates to f(n) for f =A008833,A048675,A267116;making use ofA003986.

Subsequences:A016051,A145204\{0},A329575.

Bijections are defined that relate toA003159,A005408,A007417,A036668,A088828,A088829,A299174,A325424.

Sequence in context:A095359A048724A292682*A334079A328403A199126

Adjacent sequences:A334745A334746A334747*A334749A334750A334751

nonn,easy

Peter Munn,May 09 2020

approved