A066481 -id:A066481 - cp's OEIS frontend

A222565 Primes that are the largest anti-divisor of primes.

2, 3, 5, 7, 11, 13, 19, 29, 31, 41, 47, 53, 59, 67, 71, 73, 101, 109, 127, 131, 149, 151, 167, 179, 181, 211, 233, 239, 281, 293, 307, 311, 347, 349, 379, 401, 409, 421, 431, 439, 449, 461, 467, 479, 541, 547, 569, 571, 587, 607, 613, 619, 631, 647, 661, 673, 701

Offset: 1

Juri-Stepan Gerasimov, Feb 25 2013

nonn

See A066272 for definition of anti-divisor.

Primes p such that 2p + largest anti-divisor of 2p is also prime: 2, 5, 7, 11, 13, 29, 31, 41, 47, 59, 67, 79, 83, 101, 137, 139, 151, 157, 167, 173, 193, 223, 227, 239, 257,...

			The prime 19 is here because it is largest anti-divisor of prime 29.

Paolo P. Lava, Table of n, a(n) for n = 1..1000

Cf. A066481.

is(n)=isprime(n)&&isprime(bitor((3*n-1)\2,1)) \\ Charles R Greathouse IV, Feb 27 2013

2 together with primes of the form 4k+1 such that 6k+1 is prime, together with primes of the form 4k+3 such that 6k+5 is prime. - Charles R Greathouse IV, Feb 27 2013

Missing terms a(9), a(21), a(28), a(29) added by Charles R Greathouse IV, Feb 27 2013

A066482 The smallest anti-divisor of n.

Original entry on oeis.org

2, 3, 2, 4, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 4, 2, 3, 2, 3, 2, 7, 2, 3, 2, 3, 2, 4, 2, 3, 2, 3, 2, 8, 2, 3, 2, 3, 2, 4, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 4, 2, 3, 2, 3, 2, 7, 2, 3, 2, 3, 2, 4, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 4, 2, 3, 2, 3, 2, 8, 2, 3, 2, 3, 2, 4, 2, 3, 2, 3, 2, 64, 2, 3, 2, 3

Offset: 3

Robert G. Wilson v, Jan 02 2002

nonn

Almost identical to A007978, least non-divisor of n, but there are some subtle differences.

See A066272 for definition of anti-divisor.

Seiichi Manyama, Table of n, a(n) for n = 3..10000

Cf. A066481.

antid[n_] := Select[ Union[ Join[ Select[ Divisors[2n - 1], OddQ[ # ] && # != 1 &], Select[ Divisors[2n + 1], OddQ[ # ] && # != 1 &], 2n/Select[ Divisors[2*n], OddQ[ # ] && # != 1 &]]], # < n & ]; Table[ First[ antid[n]], {n, 3, 100} ]

A216982 Anti-Chowla's function: sum of anti-divisors of n except the largest.

Original entry on oeis.org

0, 0, 0, 0, 2, 0, 5, 3, 2, 7, 5, 5, 10, 7, 8, 3, 17, 16, 5, 11, 8, 21, 19, 7, 22, 7, 24, 27, 5, 16, 21, 37, 26, 7, 29, 8, 25, 45, 26, 28, 14, 38, 27, 11, 56, 27, 29, 24, 39, 47, 8, 59, 53, 16, 37, 19, 36, 57, 51, 67, 16, 37, 70, 3, 41, 42, 87, 67, 8, 55

Offset: 1

Juri-Stepan Gerasimov, Feb 19 2013

nonn

Numbers n such that Chowla's function(n) = a(n): 1, 2, 3, 10, 15, 28, 75, 88, 231, 284, 602,...
Places n where a(n) is zero: 1, 2, 3, 4, 6, 96,...
Fixed points of this sequence: 17, 53, 127, 217, 385, 2321,...
Places n where a(n) equals the largest anti-divisor: 1, 2, 7, 10, 31, 37, 39, 55, 78, 160, 482, 937, 1599, 2496,...
Numbers n such that n -/+ 1 and a(n -/+ 1) are all primes: 6, 18, 72, 102, 108, 198, 270, 432, 570, 882,...

			Anti-divisors of 7 are 2, 3, 5, so a(7) = 2 + 3 = 5.

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Cf. A048050, A066272, A066417, A066481, A130799, A218767.

A216982 := proc(n)
        A066417(n)-A066481(n) ;
end proc: # R. J. Mathar, Feb 23 2013

a(n)=if(n<5,0,my(k=valuation(n, 2)); sigma(2*n+1)+sigma(2*n-1)+sigma(n>>k)<<(k+1)-2-20*n\/3) \\ Charles R Greathouse IV, Mar 05 2013

a(n) = A066417(n) - A066481(n).

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A222565 Primes that are the largest anti-divisor of primes.

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A066482 The smallest anti-divisor of n.

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A216982 Anti-Chowla's function: sum of anti-divisors of n except the largest.

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