A336556 - OEIS

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A336556

a(n) = 1 if A336456(n) = Product_{p^e|n} A336456(p^e), and 0 otherwise. Here each p^e is the maximal power of prime p that divides k, and A336456(n) = A335915(sigma(sigma(n))).

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

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OFFSET

LINKS

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

Index entries for characteristic functions

FORMULA

For all n >= 1, a(n) >= A336546(n).

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); };

A000265(n) = (n>>valuation(n, 2));

A335915(n) = { my(f=factor(n)); prod(k=1, #f~, if(2==f[k, 1], 1, (A000265((f[k, 1]^2)-1)^f[k, 2]))); };

A336456(n) = A335915(sigma(sigma(n)));

A336556(n) = is_fun_mult_on_n(A336456, n);

CROSSREFS

Cf. A336557 (positions of ones), A336558 (positions of zeros), A336559, A336560.

Cf. A336456, A336546.

a(n) differs from A122261(1+n) for the first time at n=28, where a(28) = 1, while A122261(1+28) = 0.

Sequence in context: A357731 A336546 A209929 * A105586 A202022 A136522

Adjacent sequences: A336553 A336554 A336555 * A336557 A336558 A336559

KEYWORD

nonn

AUTHOR

Antti Karttunen, Jul 25 2020

STATUS

approved