cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A353761 a(n) = gcd(A353749(n), A353750(n)), where A353749(n) = phi(n)*A064989(n), and A353750(n) = A353749(sigma(n)).

Original entry on oeis.org

1, 1, 2, 2, 4, 4, 2, 4, 12, 12, 2, 4, 6, 2, 16, 2, 8, 24, 6, 24, 8, 2, 2, 16, 30, 12, 48, 60, 4, 48, 2, 16, 8, 16, 8, 24, 18, 6, 24, 48, 40, 8, 14, 20, 48, 2, 2, 4, 6, 60, 32, 6, 4, 48, 24, 24, 24, 4, 2, 96, 30, 2, 48, 2, 48, 8, 2, 16, 8, 24, 2, 96, 36, 36, 60, 36, 4, 48, 6, 24, 2, 40, 2, 240, 96, 14, 16, 8, 8, 288
Offset: 1

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Author

Antti Karttunen, May 10 2022

Keywords

Links

Crossrefs

Cf. A000010, A000203, A006872, A062401, A064989, A336549, A336550, A353757, A353762, A353763.

Programs

  • PARI
    A064989(n) = { my(f=factor(n>>valuation(n,2))); for(i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f); };
A353749(n) = (eulerphi(n)*A064989(n));
A353761(n) = { my(s=sigma(n)); gcd(A353749(s), A353749(n)); };

Formula

a(n) = gcd(A353749(n), A353750(n)) = gcd(A353749(n), A353757(n)) = gcd(A353750(n), A353757(n)).
a(n) = A353749(n) / A353762(n) = A353750(n) / A353763(n).

A353762 a(n) = A353749(n) / gcd(A353749(n), A353750(n)).

Original entry on oeis.org

1, 1, 2, 1, 3, 1, 15, 1, 2, 1, 35, 2, 22, 15, 3, 4, 26, 1, 51, 1, 15, 35, 209, 1, 6, 11, 3, 1, 161, 1, 435, 1, 35, 13, 45, 2, 62, 51, 22, 1, 37, 15, 123, 7, 6, 209, 989, 8, 175, 3, 26, 44, 611, 3, 35, 5, 51, 161, 1537, 1, 118, 435, 15, 16, 33, 35, 2013, 26, 209, 15, 2345, 1, 142, 31, 12, 17, 525, 11, 949, 4, 432
Offset: 1

Views

Author

Antti Karttunen, May 10 2022

Keywords

Comments

Numerator of ratio A353749(n) / A353750(n).

Links

Crossrefs

Cf. A000010, A000203, A006872, A062401, A064989, A336549, A336550, A353757, A353761, A353763 (denominators), A353764 (positions of 1's).

Programs

  • PARI
    A064989(n) = { my(f=factor(n>>valuation(n,2))); for(i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f); };
A353749(n) = (eulerphi(n)*A064989(n));
A353762(n) = { my(s=sigma(n), u=A353749(n)); (u / gcd(A353749(s), u)); };

Formula

a(n) = A353749(n) / A353761(n) = A353749(n) / gcd(A353749(n), A353750(n)).

A353765 Numbers k for which A353749(k) is a multiple of A353749(sigma(k)), where A353749(k) = phi(k) * A064989(k), and A064989 shifts the prime factorization one step towards lower primes.

Original entry on oeis.org

1, 3, 5, 15, 27, 459, 819, 2295, 13923, 69615, 361179, 3282147, 6140043, 16410735, 30700215, 99558459, 277788987, 497792295, 1388944935
Offset: 1

Views

Author

Antti Karttunen, May 10 2022

Keywords

Comments

Question: Does every term need to be odd? Could there be any other non-multiples of 3 than a(1) and a(3)?
If it exists, a(20) > 2^32.

Links

Crossrefs

Cf. A000010, A000203, A006872, A062401, A064989, A336549, A336550, A353757, A353761.
Positions of 1's in A353763. Cf. also A353764.
Conjectured to be a subsequence of A353758.
Showing 1-3 of 3 results.

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