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.

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

Links

Antti Karttunen, Table of n, a(n) for n = 1..100000

Index entries for characteristic functions

Index entries for sequences related to primorial base

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. A003415, A038548, A276086, A329041, A358235.

Cf. also A358670.

Sequence in context: A014191 A014086 A014163 * A308016 A166360 A204183

Adjacent sequences: A358669 A358670 A358671 * A358673 A358674 A358675

Keyword

nonn,base

Author

Antti Karttunen, Nov 26 2022

Status

approved