A182088 Carmichael numbers of the form C = (30n-29)*(60n-59)*(90n-89)*(180n-179), where n is a natural number.

31146661, 2414829781, 192739365541, 197531244744661, 741700610203861, 973694665856161, 2001111155103061, 2278278996452641, 4271903575869601, 11861640972220321

Offset

1,1

Comments

Note that in this sequence, 30n-29, 60n-59, 90n-89 and 180n-179 do not have to be prime.

Conjecture: The number C = (30n-29)*(60n-59)*(90n-89)*(180n-179) is a Carmichael number if (but not only if) 30n-29, 60n-59, 90n-89 and 180n-179 are all four prime numbers.

The conjecture is checked for 0<n<150; the condition is satisfied just for n = 10, 52, 77, 143.

We got Carmichael numbers with more than three prime divisors for n = 2, 4, 72, 92, 95, 111.

Links

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

Prog

(PARI) K(n, c)=my(f=factor(c)); for(i=1, #f[, 1], if(f[i, 2]>1||(n-1)%(f[i, 1]-1), return(0))); 1
list(lim)=my(v=List(), C, n=1); while(n++ && (C=(30*n-29)*(60*n-59)*(90*n-89)*(180*n-179))<=lim, if(K(C, 30*n-29) && K(C, 60*n-59) && K(C, 90*n-89) && K(C, 180*n-179), listput(v, C))); Vec(v) \\ Charles R Greathouse IV, Jun 30 2017

Crossrefs

Cf. A002997 (Carmichael numbers).

Sequence in context: A103576 A288087 A203276 * A209786 A251530 A125574

Adjacent sequences: A182085 A182086 A182087 * A182089 A182090 A182091

Keyword

nonn

Author

Marius Coman, Apr 11 2012

Status

approved