A377870 - OEIS

%I #8 Nov 10 2024 17:09:16

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

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

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

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

%H Antti Karttunen, <a href="/A377870/b377870.txt">Table of n, a(n) for n = 1..100000</a>

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

%H <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>

%F a(n) = A359550(n) * A377868(n).

%o (PARI)

%o A359550(n) = { my(f=factor(n)); for(i=1, #f~, if(f[i, 1] <= f[i, 2], return(0))); return(1); }; \\ After code in A048103

%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 A377868(n) = if(isprime(n), 1, my(x=A276085(n),pp); forprime(p=2,, pp = p^p; if(!(x%pp), return(0)); if(pp > x, return(1))));

%o A377870(n) = (A359550(n) && A377868(n));

%Y Characteristic function of A377871.

%Y Cf. A276085, A359550, A377868.

%K nonn

%O 1

%A _Antti Karttunen_, Nov 10 2024