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Difference between n and the index of its largest prime factor: a(n) = n - A061395(n).
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%I #15 Mar 04 2024 01:36:26

%S 1,1,1,3,2,4,3,7,7,7,6,10,7,10,12,15,10,16,11,17,17,17,14,22,22,20,25,

%T 24,19,27,20,31,28,27,31,34,25,30,33,37,28,38,29,39,42,37,32,46,45,47,

%U 44,46,37,52,50,52,49,48,42,57,43,51,59,63,59,61,48,61,60

%N Difference between n and the index of its largest prime factor: a(n) = n - A061395(n).

%C All terms are strictly positive because A006530(n) <= n, A049084(n) < n and thus A061395(n) < n. [As A061395(n) = A049084(A006530(n))].

%C Please see also the comments at A243289.

%H Antti Karttunen, <a href="/A243291/b243291.txt">Table of n, a(n) for n = 1..8192</a>

%F a(n) = n - A061395(n).

%F For n > 1, a(2^n) = (2^n)-1.

%t a[n_] := n - PrimePi[FactorInteger[n][[-1, 1]]]; Array[a, 100] (* _Amiram Eldar_, Mar 04 2024 *)

%o (Scheme) (define (A243291 n) (- n (A061395 n)))

%Y Cf. A006530, A049084, A061395, A243289, A243290.

%K nonn

%O 1,4

%A _Antti Karttunen_, Jun 04 2014