%I #26 Oct 13 2024 19:02:48
%S 1,1,2,3,4,2,5,7,8,4,9,6,11,5,8,13,16,8,17,12,10,9,19,14,23,11,25,15,
%T 27,8,29,31,18,16,20,24,32,17,22,28,37,10,41,27,32,19,43,26,47,23,32,
%U 33,49,25,36,35,34,27,53,24,59,29,40,61,44,18,64,48,38,20,67,56,71,32,46,51
%N a(1) = 1. Replace each prime power in the prime factorization of n with the next lower prime power.
%e 50 = 2^1 *5^2. 1 is the prime power closest to 2 and smaller than 2. 23 is the prime power closest to 5^2 and smaller than 5^2. So a(50) = 1*23 = 23.
%o (PARI) { a(n) = local(f, r, k, d); f=factorint(n); r=1; for(i=1, matsize(f)[1], k=f[i, 1]^f[i, 2]-1; while(k>1 && !isprime(k) && (!ispower(k,,&d)||!isprime(d)), k--); r*=k); r } \\ _Max Alekseyev_, Mar 26 2007
%o (Sage) def A120636(n): return prod((previous_prime_power(p**m) for p,m in factor(n))) if n > 1 else 1 # _D. S. McNeil_, Feb 09 2011
%Y Cf. A120635.
%K nonn,mult
%O 1,3
%A _Leroy Quet_, Jun 22 2006
%E More terms from _Max Alekseyev_, Mar 26 2007