A340075 The odd part of A340072(n).

1, 1, 1, 3, 1, 1, 1, 9, 5, 3, 1, 3, 1, 5, 3, 27, 1, 5, 1, 9, 5, 3, 1, 9, 7, 1, 25, 15, 1, 3, 1, 81, 3, 9, 15, 15, 1, 11, 1, 27, 1, 5, 1, 9, 5, 7, 1, 27, 11, 21, 9, 3, 1, 25, 1, 45, 11, 15, 1, 9, 1, 9, 25, 243, 3, 3, 1, 27, 7, 3, 1, 45, 1, 5, 21, 33, 15, 1, 1, 81, 125, 21, 1, 15, 9, 23, 15, 27, 1, 15, 5, 21, 9, 13, 33, 81

Offset

1,4

Comments

Each term a(n) is a multiple of A340149(n), therefore, as both sequences have only positive terms, it follows that if a(n) = 1 then A340149(n) = 1 also, but not necessarily vice versa.

Links

Antti Karttunen, Table of n, a(n) for n = 1..8191

Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Index entries for sequences computed from indices in prime factorization

Formula

a(n) = A000265(A340072(n)).

a(n) = A339904(n) / A340074(n) = A339904(n) / gcd(A003961(n)-1, A339904(n)).

For all n >= 0, a(A019565(n)) = A339901(n).

Prog

(PARI)
A000265(n) = (n>>valuation(n, 2));
A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A340072(n) = { my(x=A003961(n), u=eulerphi(x)); u/gcd(x-1, u); };
A340075(n) = A000265(A340072(n));

Crossrefs

Cf. A000265, A003961, A019565, A339901, A339904, A340072, A340074, A340076 (positions of ones), A340149 (differs from the first time at n=85).

Sequence in context: A327564 A243748 A340149 * A307847 A080214 A263383

Adjacent sequences: A340072 A340073 A340074 * A340076 A340077 A340078

Keyword

nonn

Author

Antti Karttunen, Dec 28 2020

Status

approved