A336546 a(n) = 1 if for 1 <= i < j <= h, all sigma(p_i^e_i), sigma(p_j^e_j) are pairwise coprime, otherwise 0. Here n = p_1^e_1 * ... * p_h^e_h, where each p_i^e_i is the maximal power of prime p_i dividing n.

1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0

Offset

1

Comments

a(n) = 1 if A051027(n) is equal to A353802(n) = Product_{p^e||n} A051027(p^e), and 0 otherwise. Here each p^e is the maximal prime power divisor of n, and A051027(n) = sigma(sigma(n)).

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for characteristic functions

Index entries for sequences related to sigma(n)

Formula

a(n) = [A336562(n) == 0].

For all n >= 1, a(n) <= A336556(n).

a(n) = 1 => A336355(n) = 0.

From Antti Karttunen, May 09 2022: (Start)

In all three formulas, [ ] stands for the Iverson brackets, yielding 1 only when the two sequences obtain an equal value at n, and 0 otherwise:

a(n) = [A000203(n) == A353783(n)].

a(n) = [A051027(n) == A353802(n)].

a(n) = [A062401(n) == A353752(n)].

(End)

Prog

(PARI)
is_fun_mult_on_n(fun, n) = { my(f=factor(n)); prod(k=1, #f~, fun(f[k, 1]^f[k, 2]))==fun(n); };
A051027(n) = sigma(sigma(n));
A336546(n) = is_fun_mult_on_n(A051027, n);
(PARI) A336546(n) = { my(f=factor(n)); (sigma(n)==lcm(vector(#f~, k, sigma(f[k, 1]^f[k, 2])))); }; \\ Antti Karttunen, May 09 2022

Crossrefs

Characteristic function of A336547 (gives positions of 1's). Cf. also its complement A336548 (positions of 0's).

Cf. A000203, A051027, A062401, A065300, A324892, A336355, A336356, A336556, A336562, A353752, A353783, A353802.

Sequence in context: A054527 A137794 A357731 * A209929 A336556 A105586

Adjacent sequences: A336543 A336544 A336545 * A336547 A336548 A336549

Keyword

nonn

Author

Antti Karttunen, Jul 25 2020

Extensions

The old definition moved to comments and replaced with a more generic, but equivalent definition by Antti Karttunen, May 09 2022

Status

approved