A181816 - OEIS

%I #16 Jul 07 2019 13:36:18

%S 1,1,1,2,1,2,1,2,12,1,4,2,12,1,4,2,12,1,4,24,2,360,8,12,1,4,24,2,360,

%T 8,12,1,4,24,2,360,8,144,12,1,48,4,720,16,24,2,360,8,144,12,1

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

%C All terms also belong to A181818. Each member of A181818 appears infinitely often. a(A025487(m)) = a(A025487(n)) iff A025487(m) and A025487(n) have the same odd part (cf. A000265).

%H Amiram Eldar, <a href="/A181816/b181816.txt">Table of n, a(n) for n = 1..10000</a>

%F If A025487(n) = Product p(i)^e(i), then a(n) = Product A002110(i-1)^e(i); i.e., a(n) = A181811(A025487(n)).

%F a(n) = A181817(n)/A025487(n).

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

%Y Cf. A000265, A025487, A181811, A181817, A181818.

%K nonn

%O 1,4

%A _Matthew Vandermast_, Nov 30 2010