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Number of divisors d of n such that A049820(d) > 0 and A049820(d) is also a divisor of n.
3

%I #13 Jan 07 2019 11:13:11

%S 0,0,1,1,0,2,0,2,1,0,0,4,0,0,2,2,0,3,0,1,1,0,0,5,0,0,1,1,0,4,0,2,1,0,

%T 1,6,0,0,1,2,0,2,0,1,2,0,0,6,0,0,1,1,0,3,0,2,1,0,0,6,0,0,1,2,0,2,0,1,

%U 1,2,0,7,0,0,2,1,0,2,0,2,1,0,0,4,0,0,1,2,0,5,0,1,1,0,0,6,0,0,2,1,0,2,0,2,3

%N Number of divisors d of n such that A049820(d) > 0 and A049820(d) is also a divisor of n.

%C Records 0, 1, 2, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 19, 20, 22, 27, 30, ... occur at n = 1, 3, 6, 12, 24, 36, 72, 144, 240, 360, 720, 1440, 1680, 2640, 3360, 5040, 7920, 10080, 30240, 55440, ...

%H Antti Karttunen, <a href="/A323068/b323068.txt">Table of n, a(n) for n = 1..10080</a>

%F Sum_{d|n} [A049820(d) > 0 and A049820(d)|n], where [ ] is the Iverson bracket.

%F a(n) >= A323069(n) => A322358(n).

%o (PARI) A323068(n) = sumdiv(n,d,my(t=(d-numdiv(d))); ((t>0)&&!(n%t)));

%Y Cf. A000005, A049820, A322358, A323069.

%K nonn

%O 1,6

%A _Antti Karttunen_, Jan 05 2019