A351957 a(n) = 1 if the primorial inflation of k is a sum of distinct primorial numbers, otherwise 0.

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

Offset

1

Comments

a(n) = 1 if A108951(n) is in A276156, or equally, if A324886(n) is squarefree number (in A005117), otherwise 0.

Links

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

Index entries for characteristic functions

Index entries for sequences related to primorial base

Index entries for sequences related to primorial numbers

Formula

a(n) = A008966(A324886(n)).

a(n) = 1 if A344592(n) = 1, and 0 otherwise.

For n > 1, A010051(n) = a(n) * A351956(n).

Prog

(PARI)
A034386(n) = prod(i=1, primepi(n), prime(i));
A108951(n) = { my(f=factor(n)); prod(i=1, #f~, A034386(f[i, 1])^f[i, 2]) }; \\ From A108951
A328572(n) = { my(m=1, p=2); while(n, if(n%p, m *= p^((n%p)-1)); n = n\p; p = nextprime(1+p)); (m); };
A344592(n) = A328572(A108951(n));
A351957(n) = (1==A344592(n));
(PARI)
\\ Alternatively:
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A324886(n) = A276086(A108951(n));
A351957(n) = issquarefree(A324886(n));
(PARI)
is_in_A276156(n) = { my(p=2); while(n, if((n%p)>1, return(0)); n = n\p; p = nextprime(1+p)); (1); };
A351957(n) = is_in_A276156(A108951(n));

Crossrefs

Characteristic function of A344591.

Cf. A005117, A008966, A108951, A276156, A324886, A328572, A344592, A351959.

Cf. also A010051, A351956.

Sequence in context: A092079 A342877 A140074 * A342004 A284881 A374048

Adjacent sequences: A351954 A351955 A351956 * A351958 A351959 A351960

Keyword

nonn

Author

Antti Karttunen, Apr 04 2022

Status

approved