|
|
|
|
1, 1, 2, 2, 3, 4, 5, 4, 3, 6, 7, 8, 11, 10, 9, 8, 13, 6, 17, 12, 15, 14, 19, 16, 5, 22, 9, 20, 23, 18, 29, 16, 21, 26, 25, 12, 31, 34, 33, 24, 37, 30, 41, 28, 27, 38, 43, 32, 7, 10, 39, 44, 47, 18, 35, 40, 51, 46, 53, 36, 59, 58, 45, 32, 55, 42, 61, 52, 57, 50, 67, 24, 71, 62, 15, 68, 49, 66, 73, 48, 27
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,3
|
|
COMMENTS
|
If the exponent of the largest prime dividing n is larger than one, subtract one from that exponent. Otherwise, shift that "lonely largest prime" one step towards smaller primes.
For any number n >= 2 in binary trees A253563 and A253565, a(n) gives the number which is the parent of n.
|
|
LINKS
|
|
|
FORMULA
|
|
|
PROG
|
(PARI) A253553(n) = if(n<=2, 1, my(f=factor(n), k=#f~); if(f[k, 2]>1, f[k, 2]--, f[k, 1] = precprime(f[k, 1]-1)); factorback(f)); \\ Antti Karttunen, Jul 17 2020
|
|
CROSSREFS
|
Cf. A252464 (the number of iterations of n -> a(n) needed to reach 1 from n.)
Cf. A052126, A122111, A241917, A243287, A252462, A252463, A253550, A253563, A253565, A336120, A336125.
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|