A120636 a(1) = 1. Replace each prime power in the prime factorization of n with the next lower prime power.

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, 27, 8, 29, 31, 18, 16, 20, 24, 32, 17, 22, 28, 37, 10, 41, 27, 32, 19, 43, 26, 47, 23, 32, 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

Offset

1,3

Links

Table of n, a(n) for n=1..76.

Example

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.

Prog

(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
(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

Crossrefs

Cf. A120635.

Sequence in context: A295887 A293450 A322990 * A209747 A117744 A366481

Adjacent sequences: A120633 A120634 A120635 * A120637 A120638 A120639

Keyword

nonn,mult

Author

Leroy Quet, Jun 22 2006

Extensions

More terms from Max Alekseyev, Mar 26 2007

Status

approved