cp's OEIS Frontend

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).

%I A253553 #14 Jul 17 2020 22:56:50
%S A253553 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,
%T A253553 23,18,29,16,21,26,25,12,31,34,33,24,37,30,41,28,27,38,43,32,7,10,39,
%U A253553 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
%N 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).
%C A253553 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.
%C A253553 For any number n >= 2 in binary trees A253563 and A253565, a(n) gives the number which is the parent of n.
%H A253553 Antti Karttunen, <a href="/A253553/b253553.txt">Table of n, a(n) for n = 1..10000</a>
%F 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).
%F A253553 a(n) = A122111(A252463(A122111(n))). - _Antti Karttunen_, Jul 14 2020
%o A253553 (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
%o A253553 (Scheme) (define (A253553 n) (cond ((<= n 1) n) ((zero? (A241917 n)) (A052126 n)) (else (A252462 n))))
%Y A253553 Cf. A252464 (the number of iterations of n -> a(n) needed to reach 1 from n.)
%Y A253553 Cf. A052126, A122111, A241917, A243287, A252462, A252463, A253550, A253563, A253565, A336120, A336125.
%K A253553 nonn
%O A253553 1,3
%A A253553 _Antti Karttunen_, Jan 12 2015