

A061898


Swap each prime in factorization of n with "neighbor" prime.


5



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
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OFFSET

1,2


COMMENTS

Here "neighbor" primes are just paired in order: 2<>3, 5<>7, 11<>13, etc. Selfinverse 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


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


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(ip1))); factorback(f); \\ Michel Marcus, Jun 09 2014


CROSSREFS

Cf. A045965.
Sequence in context: A227630 A286251 A072027 * A021756 A274925 A084398
Adjacent sequences: A061895 A061896 A061897 * A061899 A061900 A061901


KEYWORD

easy,nonn,mult


AUTHOR

Marc LeBrun, May 14 2001


STATUS

approved



