A377988 - OEIS

%I #6 Nov 18 2024 11:54:38

%S 0,0,1,1,1,1,1,1,0,1,1,0,1,1,0,0,1,1,1,0,0,1,1,1,0,1,1,0,1,1,1,1,0,0,

%T 0,1,1,1,0,1,1,1,1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,1,1,0,1,1,0,

%U 0,1,1,1,1,1,1,0,0,1,1,1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,1,1,1,1,1,0,1,1,1,1,1,0,1,1,0,1,1,1,0,0,1,1,0,1,0

%N a(n) = A359550(A003415(A276085(n))), where A359550 is multiplicative with a(p^e) = 1 if p > e, otherwise 0, A003415 is the arithmetic derivative, and A276085 is fully additive with a(p) = p#/p.

%H Antti Karttunen, <a href="/A377988/b377988.txt">Table of n, a(n) for n = 1..481</a>

%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>

%F a(n) = A359550(A373842(n)) = A368915(A276085(n)).

%F a(n) <= A377868(n).

%o (PARI)

%o A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));

%o A276085(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*prod(i=1,primepi(f[k, 1]-1),prime(i))); };

%o A359550(n) = { my(pp); forprime(p=2, , pp = p^p; if(!(n%pp), return(0)); if(pp > n, return(1))); };

%o A373842(n) = A003415(A276085(n));

%o A377988(n) = A359550(A373842(n));

%Y Characteristic function of A377989.

%Y Cf. A003415, A276085, A359550, A368915, A373842, A377868.

%K nonn

%O 1

%A _Antti Karttunen_, Nov 18 2024