A344756 -id:A344756 - cp's OEIS frontend

A345930 a(n) = A344756(A276086(n)).

1, 1, 1, 2, 7, 1, 1, 1, 1, 13, 41, 2, 9, 11, 37, 2, 47, 3, 11, 7, 43, 19, 53, 4, 13, 17, 49, 11, 59, 1, 1, 1, 1, 17, 55, 1, 1, 1, 1, 106, 317, 19, 73, 92, 289, 127, 359, 13, 87, 113, 331, 148, 401, 11, 101, 134, 373, 169, 443, 2, 11, 13, 47, 2, 61, 17, 69, 86, 277, 121, 347, 2, 83, 107, 319, 2, 389, 31, 97, 128, 19

Offset: 1

Antti Karttunen, Jul 19 2021

Antti Karttunen, Table of n, a(n) for n = 1..13860
Index entries for sequences related to primorial base

Cf. A003415, A069359, A276086, A327860, A329029, A344756, A346469.

Cf. also A342002, A346474, A346475 (compare the scatter plots).

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A069359(n) = (n*sumdiv(n, d, isprime(d)/d)); \\ From A069359
A344756(n) = { my(u=A003415(n)); (u/gcd(u,A069359(n))); };
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A345930(n) = A344756(A276086(n));

a(n) = A344756(A276086(n)).

a(n) = A327860(n) / A346469(n) = A327860(n) / gcd(A327860(n), A329029(n)).

A344696 a(n) = sigma(n) / gcd(sigma(n), A001615(n)).

Original entry on oeis.org

1, 1, 1, 7, 1, 1, 1, 5, 13, 1, 1, 7, 1, 1, 1, 31, 1, 13, 1, 7, 1, 1, 1, 5, 31, 1, 10, 7, 1, 1, 1, 21, 1, 1, 1, 91, 1, 1, 1, 5, 1, 1, 1, 7, 13, 1, 1, 31, 57, 31, 1, 7, 1, 10, 1, 5, 1, 1, 1, 7, 1, 1, 13, 127, 1, 1, 1, 7, 1, 1, 1, 65, 1, 1, 31, 7, 1, 1, 1, 31, 121, 1, 1, 7, 1, 1, 1, 5, 1, 13, 1, 7, 1, 1, 1, 21, 1, 57, 13

Offset: 1

Antti Karttunen, May 26 2021

nonn

This is not multiplicative. The first point where a(m*n) = a(m)*a(n) does not hold for coprime m and n is 108 = 4*27, where a(108) = 35, although a(4) = 7 and a(27) = 10. See A344702.

Antti Karttunen, Table of n, a(n) for n = 1..10404
Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537
Index entries for sequences related to sigma(n)

Cf. A000203, A001615, A005117 (positions of ones), A344695, A344697, A344698, A344702.

Cf. also A344756.

A001615(n) = if(1==n,n, my(f=factor(n)); prod(i=1, #f~, f[i, 1]^f[i, 2] + f[i, 1]^(f[i, 2]-1))); \\ After code in A001615
A344696(n) = { my(u=sigma(n)); (u/gcd(u,A001615(n))); };

a(n) = A000203(n) / A344695(n).

A344757 a(n) = A069359(n) / gcd(A003415(n), A069359(n)).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 5, 1, 7, 1, 1, 1, 5, 1, 1, 1, 9, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 13, 8, 1, 1, 5, 1, 7, 1, 15, 1, 5, 1, 9, 1, 1, 1, 31, 1, 1, 10, 1, 1, 1, 1, 19, 1, 1, 1, 5, 1, 1, 8, 21, 1, 1, 1, 7, 1, 1, 1, 41, 1, 1, 1, 13, 1, 31, 1, 25, 1, 1, 1, 5, 1, 9, 14, 1, 1, 1, 1, 15

Offset: 2

Antti Karttunen, May 28 2021

nonn

Antti Karttunen, Table of n, a(n) for n = 2..12012
Antti Karttunen, Data supplement: n, a(n) computed for n = 2..65537

Cf. A003415, A069359, A340070, A344756.

Cf. also A344697.

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A069359(n) = (n*sumdiv(n, d, isprime(d)/d)); \\ From A069359
A344757(n) = { my(u=A069359(n)); (u/gcd(u,A003415(n))); };

a(n) = A069359(n) / A340070(n) = A069359(n) / gcd(A003415(n), A069359(n)).

cp's OEIS Frontend

A345930 a(n) = A344756(A276086(n)).

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A344696 a(n) = sigma(n) / gcd(sigma(n), A001615(n)).

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A344757 a(n) = A069359(n) / gcd(A003415(n), A069359(n)).

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