A231814 -id:A231814 - cp's OEIS frontend

A231815 Squarefree numbers (A005117) of the form pqr with prime factors p, q, r with q = 2p-1 and r = 2q-1.

30, 51319, 3882139, 289022911, 674910259, 991523479, 1893583519, 4550912389, 9761467669, 16721570539, 28685399311, 72886214809, 77372307511, 82720376839, 98685849571, 173850108931, 220038912319, 229352039821, 240313142749, 257401051861, 428178002569

Offset: 1

Jaroslav Krizek, Nov 13 2013

nonn

Squarefree numbers of the form p*q*r, where p < q < r = primes with q = 2*p - 1 and r = 2*q - 1; that is, r = 4*p - 3.

These numbers are divisible by the arithmetic mean of their proper divisors.

			3882139 = 79*157*313; 157 = 2*79 - 1; 313 = 2*157 - 1.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A005117, A057326, A000040, A231814, A231816.

Cf. A057326 (first member of a prime triple in a 2p-1 progression).

t = {}; p = 1; Do[While[p = NextPrime[p]; ! (PrimeQ[p2 = 2 p - 1] && PrimeQ[p3 = 2 p2 - 1])]; AppendTo[t, p*p2*p3], {30}]; t (* T. D. Noe, Nov 15 2013 *)
3#-10#^2+8#^3&/@Select[Prime[Range[600]],AllTrue[{2#-1,4#-3},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Apr 02 2016 *)

A231816 a(n) = the smallest squarefree number (A005117) with n prime factors in a 2p-1 progression.

Original entry on oeis.org

2, 6, 30, 351137972965951, 8596208716179446431, 698211042943963834650959743951, 744014385572130806167897354113929551, 901203402294977554329263775346819632824908852456695769189267773301

Offset: 1

Jaroslav Krizek, Nov 13 2013

nonn

Smallest squarefree numbers with n >= 2 prime divisors of the form p_1 * p_2 * … * p_n, where p_1 < p_2 < … < p_k = primes with p_k = 2 * p_(k-1) - 1.

Subsequence of A231814.

			8596208716179446431 = 1531*3061*6121*12241*24481, where 3061 = 2*1531 - 1, 6121 = 2*3061 - 1, 12241 = 2*6121 - 1, 24481 = 2*12241 - 1.

Jaroslav Krizek, Table of n, a(n) for n = 1..15

Cf. A005117, A000040, A231814, A231815.

Cf. A057330 (first prime for such numbers that has n factors).

cp's OEIS Frontend

A231815 Squarefree numbers (A005117) of the form pqr with prime factors p, q, r with q = 2p-1 and r = 2q-1.

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A231816 a(n) = the smallest squarefree number (A005117) with n prime factors in a 2p-1 progression.

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cp's OEIS Frontend

A231815 Squarefree numbers (A005117) of the form p*q*r with prime factors p, q, r with q = 2*p-1 and r = 2*q-1.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

A231816 a(n) = the smallest squarefree number (A005117) with n prime factors in a 2p-1 progression.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

A231815 Squarefree numbers (A005117) of the form pqr with prime factors p, q, r with q = 2p-1 and r = 2q-1.