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A253553
a(1) = 1; for n>1, if A241917(n) = 0 [i.e., n is a term of A070003], a(n) = A052126(n), otherwise a(n) = A252462(n).
15
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
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
a(1) = 1; for n>1, if A241917(n) = 0 [i.e., n is a term of A070003], a(n) = A052126(n), otherwise a(n) = A252462(n).
a(n) = A122111(A252463(A122111(n))). - Antti Karttunen, Jul 14 2020
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
(Scheme) (define (A253553 n) (cond ((<= n 1) n) ((zero? (A241917 n)) (A052126 n)) (else (A252462 n))))
CROSSREFS
Cf. A252464 (the number of iterations of n -> a(n) needed to reach 1 from n.)
Sequence in context: A318285 A318560 A030385 * A031250 A031233 A030584
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jan 12 2015
STATUS
approved