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 A061898 Swap each prime in factorization of n with "neighbor" prime. 8
 1, 3, 2, 9, 7, 6, 5, 27, 4, 21, 13, 18, 11, 15, 14, 81, 19, 12, 17, 63, 10, 39, 29, 54, 49, 33, 8, 45, 23, 42, 37, 243, 26, 57, 35, 36, 31, 51, 22, 189, 43, 30, 41, 117, 28, 87, 53, 162, 25, 147, 38, 99, 47, 24, 91, 135, 34, 69, 61, 126, 59, 111, 20, 729, 77, 78, 71, 171, 58 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Here "neighbor" primes are just paired in order: 2<->3, 5<->7, 11<->13, etc. Self-inverse permutation of the integers. Multiplicative. LINKS Alois P. Heinz, Table of n, a(n) for n = 1..20000 Index entries for sequences that are permutations of the natural numbers. FORMULA Sum_{k=1..n} a(k) ~ c * n^2, where c = (1/2) * Product_{p prime} ((p^2-p)/(p^2-q(p)) = 0.9229142333..., where q(p) is the "neighbor" of p. - Amiram Eldar, Nov 29 2022 EXAMPLE a(60) = 126 since 60 = 2^2*3*5, swapping 2<->3 and 5<->7 gives 3^2*2*7 = 126 (and of course then a(126) = 60). MAPLE p:= proc(n) option remember; `if`(numtheory[pi](n)::odd, nextprime(n), prevprime(n)) end: a:= n-> mul(p(i[1])^i[2], i=ifactors(n)[2]): seq(a(n), n=1..80); # Alois P. Heinz, Sep 13 2017 MATHEMATICA p[n_] := p[n] = If[OddQ[PrimePi[n]], NextPrime[n], NextPrime[n, -1]]; a[1] = 1; a[n_] := Product[p[i[[1]]]^i[[2]], {i, FactorInteger[n]}]; Array[a, 80] (* Jean-François Alcover, Jun 10 2018, after Alois P. Heinz *) PROG (PARI) a(n) = my(f=factor(n)); for (i=1, #f~, ip = primepi(f[i, 1]); if (ip % 2, f[i, 1] = prime(ip+1), f[i, 1] = prime(ip-1))); factorback(f); \\ Michel Marcus, Jun 09 2014 CROSSREFS Cf. A045965, A275407 (fixed points). Sequence in context: A286251 A361518 A072027 * A360648 A359036 A021756 Adjacent sequences: A061895 A061896 A061897 * A061899 A061900 A061901 KEYWORD easy,nonn,look,mult AUTHOR Marc LeBrun, May 14 2001 STATUS approved

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Last modified December 7 11:41 EST 2023. Contains 367656 sequences. (Running on oeis4.)