A341609 - OEIS

%I #11 Feb 22 2021 14:24:59

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

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

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

%N Characteristic function of A337372: a(n) = 1 if A337345(n) = 1, otherwise 0.

%C Characteristic function of the primitive terms of A246282.

%H Antti Karttunen, <a href="/A341609/b341609.txt">Table of n, a(n) for n = 1..65537</a>

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

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

%F a(n) = [A337345(n) = 1], where [ ] is the Iverson bracket.

%t f[1] = 1; f[n_] := Times @@ (NextPrime[#1]^#2 & @@@ FactorInteger[n]); a[n_] := Boole[DivisorSum[n, 1 &, f[#] > 2*# &] == 1]; Array[a, 100] (* _Amiram Eldar_, Feb 22 2021 *)

%o (PARI)

%o A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };

%o A341609(n) = if(A003961(n) < 2*n, 0, fordiv(n, d, if((d<n)&&(A003961(d) > 2*d), return(0))); (1)); \\ After code in A341619

%Y Cf. A003961, A246282, A337345, A337372.

%Y Cf. also A341619.

%K nonn

%O 1

%A _Antti Karttunen_, Feb 22 2021