A158377 a(1) = 0, a(n) = lcm(A034684(n), A034699(n)) for n >= 2.

0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 10, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 14, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 15, 61, 62, 63, 64, 65, 22, 67, 68, 69, 14, 71, 72

Offset

1,2

Comments

a(n) for n >= 2 equals LCM of minimal and maximal prime power factors in prime factorization of n. For n >= 2 holds: a(n)*A100994(n) = A034684(n)*A034699(n). a(n) for n >= 2 it deviates from A000027(n), first different term is a(30)=a(2*3*5), a(30)=lcm(2,5)=10, A000027(30)= 30. Sequence of deviations from A000027(n): 30,42,60,66,70,78,84,90,...

Links

Table of n, a(n) for n=1..72.

Formula

a(1) = 0, a(p) = p, a(pq) = pq, a(pq...z) = pz, a(p^k) = p^k, for p = primes (A000040), pq = product of two distinct primes (A006881), pq...z = product of k (k > 2) distinct primes p, q, ..., z (A120944), p^k = prime powers (A000961(n) for n > 1), k = natural numbers (A000027).

Example

For n = 30 = 2*3*5, a(30) = lcm(2,5) = 10.

Crossrefs

Cf. A100994, A034684, A034699, A000027.

Sequence in context: A214701 A030542 A369062 * A167975 A008684 A188462

Adjacent sequences: A158374 A158375 A158376 * A158378 A158379 A158380

Keyword

nonn

Author

Jaroslav Krizek, Mar 17 2009

Status

approved