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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A339901 a(n) = A339971(n) / gcd(A339809(2*n), A339971(n)).

Original entry on oeis.org

1, 1, 1, 1, 1, 3, 3, 3, 1, 5, 5, 5, 15, 3, 5, 15, 1, 3, 3, 3, 1, 9, 9, 9, 15, 15, 5, 15, 9, 45, 5, 45, 1, 1, 1, 1, 3, 3, 1, 3, 5, 1, 5, 5, 5, 15, 15, 15, 3, 3, 1, 3, 9, 9, 3, 9, 1, 15, 15, 15, 15, 9, 45, 45, 1, 9, 9, 9, 9, 27, 27, 27, 45, 45, 5, 45, 135, 135, 45, 135, 9, 27, 27, 27, 3, 81, 81, 81, 135, 27, 45, 135, 405
Offset: 0

Views

Author

Antti Karttunen, Dec 28 2020

Keywords

Comments

Compare also to the scatter plot of A339898.

Links

Crossrefs

Cf. A000265, A053575, A019565, A160595, A339809, A339821, A339971, A339898, A339899, A340075, A340085.
Cf. A339973 (positions of ones).

Programs

  • PARI
    A000265(n) = (n>>valuation(n,2));
A019565(n) = { my(m=1, p=1); while(n>0, p = nextprime(1+p); if(n%2, m *= p); n >>= 1); (m); };
A339901(n) = { my(x=A019565(2*n), y=A000265(eulerphi(x))); y/gcd((x-1),y); };

Formula

a(n) = A339971(n) / A339899(n).
a(n) = A000265(A160595(A019565(2*n))).
a(n) = A340075(A019565(n)) = A340085(A019565(2*n)).

A339898 a(n) = A019565(2n)-1 mod A000265(phi(A019565(2n))).

Original entry on oeis.org

0, 0, 0, 0, 0, 2, 1, 2, 0, 2, 4, 4, 1, 5, 9, 14, 0, 2, 1, 2, 0, 2, 4, 5, 7, 8, 9, 14, 10, 32, 9, 29, 0, 0, 0, 0, 1, 2, 0, 2, 1, 0, 4, 4, 3, 11, 4, 14, 1, 2, 0, 2, 7, 5, 3, 2, 0, 2, 4, 14, 6, 20, 34, 14, 0, 2, 4, 5, 24, 20, 16, 23, 28, 41, 9, 29, 112, 68, 24, 74, 3, 11, 19, 5, 27, 2, 58, 14, 16, 50, 84, 119, 388, 356
Offset: 0

Views

Author

Antti Karttunen, Dec 28 2020

Keywords

Links

Crossrefs

Cf. A053575, A019565, A339809, A339821, A339971, A339899, A339901.
Cf. A339973 (positions of zeros).

Programs

  • PARI
    A000265(n) = (n>>valuation(n,2));
A019565(n) = { my(m=1, p=1); while(n>0, p = nextprime(1+p); if(n%2, m *= p); n >>= 1); (m); };
A339898(n) = { my(x=A019565(2*n)); ((x-1)%A000265(eulerphi(x))); };

Formula

a(n) = A339809(2*n) modulo A339971(n), where A339971(n) = A053575(A019565(2n)).

A339974 Odd primes that do not occur as the greatest prime divisor of any such odd composite k for which the odd part of phi(k) divides k-1.

Original entry on oeis.org

3, 7, 11, 19, 31, 37, 59, 61, 83, 103, 107, 131
Offset: 1

Views

Author

Antti Karttunen, Dec 27 2020

Keywords

Comments

Odd primes that do not occur as the greatest prime divisor (A006530) of any of the terms of A339880.
Naive way of computing (essentially an exhaustive search): apply A000523 to the terms of A339973, select unique values, add +2, and take the corresponding prime.
Questions: Is this sequence finite? If infinite, are there still only a finite number of 4k+1 primes (A002144) like 37 and 61?
a(13) >= 149, if it exists.

Examples

			Prime 127 is NOT a member, because there exists a squarefree composite number 10697881195 = 5*29*53*97*113*127, for which A053575(10697881195) = A336466(10697881195) = 120393, which is a divisor of 10697881195-1. Note that 10697881195 is a term of A339880, but not that of A339870.

Crossrefs

Cf. A000523, A002144, A006530, A053575, A336466, A339870, A339880, A339973.
Cf. also A339869.
Showing 1-3 of 3 results.

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