A064830 -id:A064830 - cp's OEIS frontend

A064937 Nonprimes k such that gcd(k, prime(k)^2 - 1) is 1.

1, 25, 49, 55, 77, 119, 133, 143, 155, 161, 169, 185, 187, 203, 209, 217, 221, 235, 247, 275, 287, 289, 295, 301, 325, 329, 361, 365, 371, 377, 391, 403, 407, 415, 425, 427, 437, 451, 455, 469, 473, 485, 493, 497, 505, 511, 517, 527, 529, 539, 553, 559, 583

Offset: 1

Robert G. Wilson v, Oct 26 2001

Harry J. Smith, Table of n, a(n) for n = 1..1000

Cf. A064830.

Select[ Range[600], !PrimeQ[ # ] && GCD[ #, Prime[ # ]^2 - 1] == 1 & ]

{ n=0; for (m=1, 10^9, if (isprime(m), next); if (gcd(m, prime(m)^2 - 1) == 1, write("b064937.txt", n++, " ", m); if (n==1000, return)) ) } \\ Harry J. Smith, Sep 30 2009

A064938 Nonprimes k such that k divides prime(k)^2 - 1.

Original entry on oeis.org

1, 4, 6, 8, 10, 12, 14, 20, 24, 42, 48, 60, 63, 70, 72, 80, 84, 108, 120, 124, 126, 153, 156, 182, 240, 246, 264, 286, 327, 372, 374, 440, 492, 516, 552, 1008, 1053, 1664, 1941, 2160, 2494, 3048, 3741, 4116, 4136, 4144, 4152, 5106, 5698, 6012, 6458, 6459

Offset: 1

Robert G. Wilson v, Oct 26 2001

Harry J. Smith, Table of n, a(n) for n = 1..160

Cf. A064830.

Select[ Range[10^4], !PrimeQ[ # ] && GCD[ #, Prime[ # ]^2 - 1] == # & ]

{ default(primelimit, 4294965247); n=0; for (m=1, 10^9, if (isprime(m), next); if (gcd(m, prime(m)^2 - 1) == m, write("b064938.txt", n++, " ", m); if (n==160, return)) ) } \\ Harry J. Smith, Sep 30 2009

A064936 Primes p such that gcd(p, prime(p)^2 - 1) does not equal 1.

Original entry on oeis.org

2, 3, 5, 181, 40087, 251737, 335276334037181, 115423110870118057, 115423110870118561

Offset: 1

Robert G. Wilson v, Oct 26 2001

No further terms up to 41161739. - Harvey P. Dale, Dec 23 2011
No further terms up to 250000000. - Sean A. Irvine, Aug 01 2023
From Jason Yuen, Apr 21 2024: (Start)
Primes p such that prime(p)^2 == 1 (mod p).
Prime terms of A023143 or A045924.
No further terms up to 4*10^19. (End)

			5 belongs in the sequence because gcd(5, P_5^2 -1) = gcd(5, 120) = 5.

Cf. A064830, A023143, A045924.

Do[ If[ GCD[ Prime[n], Prime[ Prime[n]]^2 - 1] != 1, Print[ Prime[n]] ], {n, 1, 10^6} ]

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A064937 Nonprimes k such that gcd(k, prime(k)^2 - 1) is 1.

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A064938 Nonprimes k such that k divides prime(k)^2 - 1.

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A064936 Primes p such that gcd(p, prime(p)^2 - 1) does not equal 1.

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