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A181811
a(n) = smallest integer that, upon multiplying any divisor of n, produces a member of A025487.
5
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).
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
KEYWORD
nonn,mult
AUTHOR
Matthew Vandermast, Nov 30 2010
STATUS
approved