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a(n) = smallest integer that, upon multiplying any divisor of n, produces a member of A025487.
5

%I #24 Jan 02 2024 18:10:24

%S 1,1,2,1,6,2,30,1,4,6,210,2,2310,30,12,1,30030,4,510510,6,60,210,

%T 9699690,2,36,2310,8,30,223092870,12,6469693230,1,420,30030,180,4,

%U 200560490130,510510,4620,6,7420738134810,60,304250263527210,210,24,9699690

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

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

%H Amiram Eldar, <a href="/A181811/b181811.txt">Table of n, a(n) for n = 1..2370</a>

%H <a href="/index/Di#divseq">Index to divisibility sequences</a>

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

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

%F a(n) = A108951(A064989(n)). - _Antti Karttunen_, Dec 31 2023

%e 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.

%o (Python)

%o from sympy import primerange, factorint

%o from operator import mul

%o from functools import reduce

%o def P(n): return reduce(mul, [i for i in primerange(2, n + 1)])

%o def a(n):

%o f = factorint(n)

%o return 1 if n==1 else (reduce(mul, [P(i)**f[i] for i in f]))//n

%o print([a(n) for n in range(1, 101)]) # _Indranil Ghosh_, May 14 2017

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

%K nonn,mult

%O 1,3

%A _Matthew Vandermast_, Nov 30 2010