A293442 -id:A293442 - cp's OEIS frontend

A331311 a(n) = A331287(n) / A331310(n).

1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 2, 1, 1, 1, 1, 1, 3, 1, 2, 1, 1, 1, 2, 1, 1, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 3, 1, 1, 2, 1, 1, 1, 2, 1, 3, 1, 2, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1, 2, 1, 3, 1, 2, 1, 1, 1, 2, 1, 1, 3, 1, 1, 1, 1, 2, 1

Offset: 1

Antti Karttunen, Jan 21 2020

nonn

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

Cf. A225546, A293442, A331287, A331310, A331312.

PARI
```
A331311(n) = (A331287(n)/A331310(n));
```

a(n) = A331287(n) / A331310(n) = gcd(n, A225546(n)) / gcd(n, A293442(n)).

A294931 Multiplicative with a(p^e) = A019565(A289813(e)).

Original entry on oeis.org

1, 2, 2, 1, 2, 4, 2, 3, 1, 4, 2, 2, 2, 4, 4, 6, 2, 2, 2, 2, 4, 4, 2, 6, 1, 4, 3, 2, 2, 8, 2, 3, 4, 4, 4, 1, 2, 4, 4, 6, 2, 8, 2, 2, 2, 4, 2, 12, 1, 2, 4, 2, 2, 6, 4, 6, 4, 4, 2, 4, 2, 4, 2, 1, 4, 8, 2, 2, 4, 8, 2, 3, 2, 4, 2, 2, 4, 8, 2, 12, 6, 4, 2, 4, 4, 4, 4, 6, 2, 4, 4, 2, 4, 4, 4, 6, 2, 2, 2, 1, 2, 8, 2, 6, 8, 4, 2, 3, 2, 8, 4, 12, 2, 8, 4, 2, 2, 4, 4

Offset: 1

Antti Karttunen, Nov 11 2017

Antti Karttunen, Table of n, a(n) for n = 1..65537
Index entries for sequences computed from exponents in factorization of n

Cf. A019565, A289813, A293442, A294932, A294933.

(define (A294931 n) (if (= 1 n) n (* (A019565 (A289813 (A067029 n))) (A294931 (A028234 n)))))

A294933 Compound filter related to base-3 expansion of the exponents in prime factorization of n: a(n) = P(A294932(n), A294931(n)), where P(n,k) is sequence A000027 used as a pairing function.

Original entry on oeis.org

1, 2, 2, 3, 2, 7, 2, 4, 3, 7, 2, 5, 2, 7, 7, 16, 2, 5, 2, 5, 7, 7, 2, 16, 3, 7, 4, 5, 2, 29, 2, 8, 7, 7, 7, 10, 2, 7, 7, 16, 2, 29, 2, 5, 5, 7, 2, 67, 3, 5, 7, 5, 2, 16, 7, 16, 7, 7, 2, 12, 2, 7, 5, 6, 7, 29, 2, 5, 7, 29, 2, 8, 2, 7, 5, 5, 7, 29, 2, 67, 16, 7, 2, 12, 7, 7, 7, 16, 2, 12, 7, 5, 7, 7, 7, 23, 2, 5, 5, 10, 2, 29, 2, 16, 29, 7, 2, 8, 2, 29, 7, 67

Offset: 1

Antti Karttunen, Nov 11 2017

nonn

For all i, j: a(i) = a(j) => A038148(i) = A038148(j).

Antti Karttunen, Table of n, a(n) for n = 1..65537
Index entries for sequences computed from exponents in factorization of n

Cf. A294931, A294932.
Cf. also A293225, A293226 and A293442 (analogous filter for base-2).
Cf. A010057, A038148, A240231.

a(n) = (1/2)*(2 + ((A294932(n) + A294931(n))^2) - A294932(n) - 3*A294931(n)).

A318470 Multiplicative with a(p^e) = A260443(e).

Original entry on oeis.org

1, 2, 2, 3, 2, 4, 2, 6, 3, 4, 2, 6, 2, 4, 4, 5, 2, 6, 2, 6, 4, 4, 2, 12, 3, 4, 6, 6, 2, 8, 2, 18, 4, 4, 4, 9, 2, 4, 4, 12, 2, 8, 2, 6, 6, 4, 2, 10, 3, 6, 4, 6, 2, 12, 4, 12, 4, 4, 2, 12, 2, 4, 6, 15, 4, 8, 2, 6, 4, 8, 2, 18, 2, 4, 6, 6, 4, 8, 2, 10, 5, 4, 2, 12, 4, 4, 4, 12, 2, 12, 4, 6, 4, 4, 4, 36, 2, 6, 6, 9, 2, 8, 2, 12, 8

Offset: 1

Antti Karttunen, Aug 30 2018

Cf. A260443, A318306, A318307.
Differs from A293442 for the first time at n=32, where a(32) = 18, while A293442(32) = 10.
Cf. also A293216, A293217, A293443, A318469.

A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From A003961
A260443(n) = if(n<2, n+1, if(n%2, A260443(n\2)*A260443(n\2+1), A003961(A260443(n\2))));
A318470(n) = factorback(apply(e -> A260443(e),factor(n)[,2]));

For all n >= 1, A001222(a(n)) = A318306(n).

cp's OEIS Frontend

A331311 a(n) = A331287(n) / A331310(n).

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A294931 Multiplicative with a(p^e) = A019565(A289813(e)).

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A294933 Compound filter related to base-3 expansion of the exponents in prime factorization of n: a(n) = P(A294932(n), A294931(n)), where P(n,k) is sequence A000027 used as a pairing function.

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Formula

A318470 Multiplicative with a(p^e) = A260443(e).

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