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A358670
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
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, 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, 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
OFFSET
1
FORMULA
a(n) = [A358233(n) == A038548(n)], where [ ] is the Iverson bracket.
PROG
(PARI)
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));
A358670(n) = { fordiv(n, d, if(d>(n/d), return(1)); if(1<A329041sq(d, n/d), return(0))); (1); };
CROSSREFS
Characteristic function of A358671.
Cf. also A358672.
Sequence in context: A209355 A141743 A268384 * A288524 A112416 A061265
KEYWORD
nonn,base
AUTHOR
Antti Karttunen, Nov 26 2022
STATUS
approved