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a(n) = 1 if for all factorizations of n as x*y, the sum x+y is carryfree when the addition is done in the primorial base, otherwise 0.
3

%I #14 Nov 29 2022 12:53:05

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

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

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

%N a(n) = 1 if for all factorizations of n as x*y, the sum x+y is carryfree when the addition is done in the primorial base, otherwise 0.

%H Antti Karttunen, <a href="/A358670/b358670.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) = [A358233(n) == A038548(n)], where [ ] is the Iverson bracket.

%o (PARI)

%o A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };

%o A327936(n) = { my(f = factor(n)); for(k=1, #f~, f[k,2] = (f[k,2]>=f[k,1])); factorback(f); };

%o A329041sq(row,col) = A327936(A276086(row)*A276086(col));

%o A358670(n) = { fordiv(n, d, if(d>(n/d), return(1)); if(1<A329041sq(d, n/d), return(0))); (1); };

%Y Characteristic function of A358671.

%Y Cf. A038548, A276086, A329041, A358233.

%Y Cf. also A358672.

%K nonn,base

%O 1

%A _Antti Karttunen_, Nov 26 2022