A181811 a(n) = smallest integer that, upon multiplying any divisor of n, produces a member of A025487.

1, 1, 2, 1, 6, 2, 30, 1, 4, 6, 210, 2, 2310, 30, 12, 1, 30030, 4, 510510, 6, 60, 210, 9699690, 2, 36, 2310, 8, 30, 223092870, 12, 6469693230, 1, 420, 30030, 180, 4, 200560490130, 510510, 4620, 6, 7420738134810, 60, 304250263527210, 210, 24, 9699690

Offset: 1

Author

Matthew Vandermast, Nov 30 2010

Keywords

• nonn
• mult

Comments

Each member of A025487 appears infinitely often, and exactly once among odd values of n. a(m) = a(n) iff A000265(m) = A000265(n).

Examples

			For any divisor d of 6 (d = 1, 2, 3, 6), 2d (2, 4, 6, 12) is always a member of A025487. 2 is the smallest integer with this relationship to 6; therefore, a(6)=2.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..2370
• Index to divisibility sequences

Crossrefs

Cf. A064989, A108951, A181812, A181813, A181816.

Programs

Python

from sympy import primerange, factorint
from operator import mul
from functools import reduce
def P(n): return reduce(mul, [i for i in primerange(2, n + 1)])
def a(n):
    f = factorint(n)
    return 1 if n==1 else (reduce(mul, [P(i)**f[i] for i in f]))//n
print([a(n) for n in range(1, 101)]) # Indranil Ghosh, May 14 2017

Formula

If n = Product p(i)^e(i), then a(n) = Product A002110(i-1)^e(i). Sequence is completely multiplicative.

a(n) = A108951(n)/n.

a(n) = A108951(A064989(n)). - Antti Karttunen, Dec 31 2023