A286628 - OEIS

%I #12 Jul 02 2017 03:58:58

%S 1,0,2,0,1,1,3,0,0,0,2,0,1,1,1,0,1,0,2,1,2,1,3,0,0,0,1,0,1,1,5,0,2,0,

%T 2,0,1,1,1,0,1,1,2,1,1,1,4,0,1,0,1,0,1,1,1,1,2,0,2,1,1,2,0,0,1,1,2,1,

%U 2,1,3,0,1,0,0,0,2,1,4,0,0,0,2,0,1,1,1,0,1,0,2,1,3,2,1,1,1,0,1,0,1,1,3,0,2,0,2,0,1,1,1,0,1,1,2,1,0,1,2,0

%N a(n) = exponent of the highest power of A000005(n) (number of divisors of n) dividing A000203(n) (sum of divisors of n), a(1) = 1.

%C a(1) = 1 by convention.

%H Antti Karttunen, <a href="/A286628/b286628.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A286561(A000203(n), A000005(n)).

%e A000005(6) = 4, A000203(6) = 12, 4^1 is the highest power of 4 which divides 12, thus a(6) = 1.

%e A000005(7) = 2, A000203(7) = 8, 2^3 is the highest power of 2 which divides 8, thus a(7) = 3.

%e A000005(8) = 4, A000203(8) = 15, 4^0 = 1 is the highest power of 4 which divides 15, thus a(8) = 0.

%o (PARI) A286628(n) = if(1==n,n,valuation(sigma(n), numdiv(n)));

%Y Cf. A000005, A000203, A051281, A054025, A286561, A286627.

%Y Cf. A049642 (positions of zeros), A003601 (of nonzeros).

%K nonn

%O 1,3

%A _Antti Karttunen_, Jun 30 2017