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).

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

Author

Antti Karttunen, Jan 12 2015

Keywords

• nonn

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

• Antti Karttunen, Table of n, a(n) for n = 1..10000

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.

Programs

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))))

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