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

1,3

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).

Links

Amiram Eldar, Table of n, a(n) for n = 1..2370

Index to divisibility sequences

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

Example

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.

Prog

(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

Crossrefs

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

Sequence in context: A284434 A306543 A243484 * A284431 A333078 A352376

Adjacent sequences: A181808 A181809 A181810 * A181812 A181813 A181814

Keyword

nonn,mult

Author

Matthew Vandermast, Nov 30 2010

Status

approved