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A358672
a(n) = 1 if for all factorizations of n as x*y, the sum (x * y') + (x' * y) is carryfree when the addition is done in the primorial base, otherwise 0. Here u' stands for A003415(u), the arithmetic derivative of u.
5
1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1
OFFSET
1
FORMULA
a(n) = [A358235(n) == A038548(n)], where [ ] is the Iverson bracket.
PROG
(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A327936(n) = { my(f = factor(n)); for(k=1, #f~, f[k, 2] = (f[k, 2]>=f[k, 1])); factorback(f); };
A329041sq(row, col) = A327936(A276086(row)*A276086(col));
A358672(n) = { fordiv(n, d, if(d>(n/d), return(1)); if(1<A329041sq((d*A003415(n/d)), (A003415(d)*(n/d))), return(0))); (1); };
CROSSREFS
Characteristic function of A358673, whose complement A358674 gives the positions of zeros.
Cf. also A358670.
Sequence in context: A014191 A014086 A014163 * A308016 A166360 A204183
KEYWORD
nonn,base
AUTHOR
Antti Karttunen, Nov 26 2022
STATUS
approved