A377988 a(n) = A359550(A003415(A276085(n))), where A359550 is multiplicative with a(p^e) = 1 if p > e, otherwise 0, A003415 is the arithmetic derivative, and A276085 is fully additive with a(p) = p#/p.

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

Offset

1

Links

Antti Karttunen, Table of n, a(n) for n = 1..481

Index entries for characteristic functions

Formula

a(n) = A359550(A373842(n)) = A368915(A276085(n)).

a(n) <= A377868(n).

Prog

(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A276085(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*prod(i=1, primepi(f[k, 1]-1), prime(i))); };
A359550(n) = { my(pp); forprime(p=2, , pp = p^p; if(!(n%pp), return(0)); if(pp > n, return(1))); };
A373842(n) = A003415(A276085(n));
A377988(n) = A359550(A373842(n));

Crossrefs

Characteristic function of A377989.

Cf. A003415, A276085, A359550, A368915, A373842, A377868.

Sequence in context: A295303 A288226 A373253 * A104121 A179770 A189078

Adjacent sequences: A377985 A377986 A377987 * A377989 A377990 A377991

Keyword

nonn

Author

Antti Karttunen, Nov 18 2024

Status

approved