|
|
A348746
|
|
Fully multiplicative with a(2) = 3, a(3) = 5, a(A002144(n)) = A002144(1+n) and a(A002145(1+n)) = a(A002145(1+n)) for all n >= 1, where A002144 and A002145 give the primes of the form 4k+1 and 4k+3 respectively.
|
|
9
|
|
|
1, 3, 5, 9, 13, 15, 7, 27, 25, 39, 11, 45, 17, 21, 65, 81, 29, 75, 19, 117, 35, 33, 23, 135, 169, 51, 125, 63, 37, 195, 31, 243, 55, 87, 91, 225, 41, 57, 85, 351, 53, 105, 43, 99, 325, 69, 47, 405, 49, 507, 145, 153, 61, 375, 143, 189, 95, 111, 59, 585, 73, 93, 175, 729, 221, 165, 67, 261, 115, 273, 71, 675, 89, 123
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
Permutation of odd numbers. Preserves the prime signature.
|
|
LINKS
|
|
|
FORMULA
|
Fully multiplicative with a(p) = A348744(A000720(p)), where A348744 is the lexicographically earliest bijection from primes to odd primes where each prime of the form 4k+1 is mapped to the next larger prime of the same form.
|
|
PROG
|
(PARI) A348746(n) = { my(f=factor(n)); for(k=1, #f~, if(2==f[k, 1], f[k, 1]=3, if(3==f[k, 1], f[k, 1]=5, if(1==(f[k, 1]%4), for(i=1+primepi(f[k, 1]), oo, if(1==(prime(i)%4), f[k, 1]=prime(i); break)))))); factorback(f); };
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,mult
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|