cp's OEIS Frontend

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

%I A181811 #24 Jan 02 2024 18:10:24
%S A181811 1,1,2,1,6,2,30,1,4,6,210,2,2310,30,12,1,30030,4,510510,6,60,210,
%T A181811 9699690,2,36,2310,8,30,223092870,12,6469693230,1,420,30030,180,4,
%U A181811 200560490130,510510,4620,6,7420738134810,60,304250263527210,210,24,9699690
%N A181811 a(n) = smallest integer that, upon multiplying any divisor of n, produces a member of A025487.
%C A181811 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 A181811 Amiram Eldar, <a href="/A181811/b181811.txt">Table of n, a(n) for n = 1..2370</a>
%H A181811 <a href="/index/Di#divseq">Index to divisibility sequences</a>
%F A181811 If n = Product p(i)^e(i), then a(n) = Product A002110(i-1)^e(i). Sequence is completely multiplicative.
%F A181811 a(n) = A108951(n)/n.
%F A181811 a(n) = A108951(A064989(n)). - _Antti Karttunen_, Dec 31 2023
%e A181811 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 A181811 (Python)
%o A181811 from sympy import primerange, factorint
%o A181811 from operator import mul
%o A181811 from functools import reduce
%o A181811 def P(n): return reduce(mul, [i for i in primerange(2, n + 1)])
%o A181811 def a(n):
%o A181811     f = factorint(n)
%o A181811     return 1 if n==1 else (reduce(mul, [P(i)**f[i] for i in f]))//n
%o A181811 print([a(n) for n in range(1, 101)]) # _Indranil Ghosh_, May 14 2017
%Y A181811 Cf. A064989, A108951, A181812, A181813, A181816.
%K A181811 nonn,mult
%O A181811 1,3
%A A181811 _Matthew Vandermast_, Nov 30 2010