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 A334748 Let p be the smallest odd prime not dividing the squarefree part of n. Multiply n by p and divide by the product of all smaller odd primes. 3
 3, 6, 5, 12, 15, 10, 21, 24, 27, 30, 33, 20, 39, 42, 7, 48, 51, 54, 57, 60, 35, 66, 69, 40, 75, 78, 45, 84, 87, 14, 93, 96, 55, 102, 105, 108, 111, 114, 65, 120, 123, 70, 129, 132, 135, 138, 141, 80, 147, 150, 85, 156, 159, 90, 165, 168, 95, 174, 177, 28, 183, 186, 189 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS A permutation of A028983. A007417 (which has asymptotic density 3/4) lists index n such that a(n) = 3n. The sequence maps the terms of A007417 1:1 onto A145204\{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) to A088829, from A003159 to the nonsquares in A003159, and from A325424 to the nonsquares in A036668. The latter two bijections are between sets where membership depends on whether a number's squarefree part divides by 2 and/or 3. LINKS FORMULA 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 operation A003986. a(A007417(n)) = A145204(n+1) = 3 * A007417(n). EXAMPLE 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. PROG (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 CROSSREFS Permutation of A028983. Row 3, and therefore column 3, of A331590. Cf. A334747 (row 2). A007913, A034386, A225546, A284723 are used in formulas defining the sequence. The formula section details how the sequence maps the terms of A003961, A019565, A070826; and how f(a(n)) relates to f(n) for f = A008833, A048675, A267116; making use of A003986. Subsequences: A016051, A145204\{0}, A329575. Bijections are defined that relate to A003159, A005408, A007417, A036668, A088828, A088829, A299174, A325424. Sequence in context: A095359 A048724 A292682 * A334079 A328403 A199126 Adjacent sequences:  A334745 A334746 A334747 * A334749 A334750 A334751 KEYWORD nonn,easy AUTHOR Peter Munn, May 09 2020 STATUS approved

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Last modified May 7 19:09 EDT 2021. Contains 343652 sequences. (Running on oeis4.)