A395053 - OEIS

%I #7 Apr 15 2026 13:36:06

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

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

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

%N a(n) = 1 if the greatest prime dividing A276085(n) is larger than the greatest prime dividing n, otherwise 0, where A276085 is fully additive with a(p) = p#/p. a(1) = 0 by convention.

%H Antti Karttunen, <a href="/A395053/b395053.txt">Table of n, a(n) for n = 1..10000</a>

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

%F a(n) = [n>1 and A395052(n) > A006530(n)], where [ ] is the Iverson bracket.

%o (PARI)

%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 A395053(n) = if(n<=1 || isprime(n), 0, my(f = factor(n), gpf = vecmax(f[, 1]), x = A276085(n)); forprime(p=2, gpf, x /= (p^valuation(x,p))); (x>1));

%Y Characteristic function of A395054.

%Y Cf. A006530, A276085, A395052, A395055.

%Y Cf. also A395043.

%K nonn,easy

%O 1

%A _Antti Karttunen_, Apr 15 2026