A373367 a(n) is the greatest common divisor of A001414(n), A003415(n), and A276085(n).

0, 1, 1, 2, 1, 1, 1, 3, 2, 7, 1, 1, 1, 1, 8, 4, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 3, 1, 1, 1, 1, 5, 2, 1, 12, 2, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 4, 1, 1, 1, 8, 1, 2, 1, 1, 2, 1, 1, 1, 6, 6, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 6, 1, 1, 1, 4, 1, 1, 2, 2, 1, 8, 1, 1, 1, 20, 1, 2, 1, 12, 1, 1, 1, 1, 14, 1, 1, 1, 1, 1

Offset

1,4

Comments

All sequences that give the positions of multiples of some natural number k in this sequence are closed under multiplication because the constituent sequences A001414, A003415, and A276085 also have the same property.

A345452 gives the positions of even terms in this sequence, because it gives them for A373362, and because for A373145 and A373364 the positions of even terms are given by A368998 (union of A345452 and 2*A358776) and A373375 (union of A345452 and 8*A345452), thus both are supersets of A345452.

Links

Antti Karttunen, Table of n, a(n) for n = 1..100000

Formula

a(n) = gcd(A373145(n), A373362(n)) = gcd(A373145(n), A373364(n)) = gcd(A373362(n), A373364(n)).

Prog

(PARI)
A001414(n) = ((n=factor(n))[, 1]~*n[, 2]); \\ From A001414.
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))); };
A373367(n) = gcd([A001414(n), A003415(n), A276085(n)]);

Crossrefs

Cf. A001414, A003415, A276085, A345452 (gives the positions of even terms).

Greatest common divisor of any two of these three: A373145, A373362, A373364.

Sequence in context: A136043 A336420 A254055 * A373362 A373145 A096815

Adjacent sequences: A373364 A373365 A373366 * A373368 A373369 A373370

Keyword

nonn

Author

Antti Karttunen, Jun 03 2024

Status

approved