A182206 Carmichael numbers of the form C = 37*73*(18n+91).

294409, 488881, 1461241, 2433601, 2628073, 16046641, 69331969, 105309289, 109393201, 509033161, 672389641, 885336481, 1074363265, 1103145121, 1232469001, 1384157161, 1674309385, 1760460481, 1836304561, 1854001513, 2073560401, 3240392401

Offset

1,1

Comments

We got Carmichael numbers for n = 1, 5, 25, 49, 325, 1421, 2161, 2245, 10465, 18205, 22685, 25345, 34433, 36205, 37765, 38129, 42645, 89565, 104173, 119509, 134725, 186101.

Conjecture: Any Carmichael number C divisible by 37 and 73 can be written as C = 37*73*(18n+91), where n is natural; checked for the first 22 Carmichael numbers divisible by 37 and 73.

This follows from Korselt's criterion. More is true: such numbers are 37*73*(72k+1). - Charles R Greathouse IV, Oct 02 2012

Links

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

Eric Weisstein's World of Mathematics, Carmichael Number

Prog

(PARI) Korselt(n)=my(f=factor(n)); for(i=1, #f[, 1], if(f[i, 2]>1||(n-1)%(f[i, 1]-1), return(0))); 1
list(lim)=my(v=List()); forstep(n=294409, lim, 194472, if(Korselt(n), listput(v, n))); Vec(v) \\ Charles R Greathouse IV, Jun 30 2017

Crossrefs

Sequence in context: A328664 A328935 A335584 * A178997 A328938 A291637

Adjacent sequences: A182203 A182204 A182205 * A182207 A182208 A182209

Keyword

nonn

Author

Marius Coman, Apr 18 2012

Extensions

Terms corrected by Charles R Greathouse IV, Oct 02 2012

Status

approved