A256545 Composite numbers k such that k*phi(k) is in A002378.

6, 30, 434, 510, 616, 912, 1640, 2989, 3003, 5934, 7280, 8600, 10726, 12700, 13825, 14288, 18699, 19389, 54153, 59394, 59906, 70563, 72816, 116052, 117964, 121954, 131070, 134212, 140752, 177000, 206514, 210728, 274023, 319522, 418610, 437736, 456666

Offset

1,1

Comments

Composite k such that 4*A002618(k)+1 is a square.

For all primes p, 4*A002618(p) + 1 = (2*p-1)^2.

The only semiprime < 10^7 in the sequence is 6.

k = 2*p with p prime is in the sequence if 2*p-1 is in A001653. However, the only such p < 10^3000 is 3.

Similarly, k = 3*p with p prime is in the sequence if 2*p-1 is in A080806. However, the only such p < 10^3000 is 2.

Links

Amiram Eldar, Table of n, a(n) for n = 1..258 (terms below 10^11; terms 1..62 from Robert Israel)

Example

a(1) = 6 is in the sequence because 6*phi(6) = 12 = 4*3.

Maple

select(n -> not isprime(n) and issqr(1+4*n*numtheory:-phi(n)), [$1..10^6]);

Mathematica

Select[Range[10^6], !PrimeQ[#]&&IntegerQ[Sqrt[4*#*EulerPhi[#]+1]]&] (* Ivan N. Ianakiev, Apr 02 2015 *)

Prog

(PARI) lista(nn) = {forcomposite (n=1, nn, if (ispolygonal(n*eulerphi(n)/2, 3), print1(n ", ")); ); } \\ Michel Marcus, Apr 02 2015

Crossrefs

Cf. A000010, A001653, A002378, A002618, A080806.

Sequence in context: A369135 A111876 A119634 * A349981 A075591 A130075

Adjacent sequences: A256542 A256543 A256544 * A256546 A256547 A256548

Keyword

nonn

Author

Robert Israel, Apr 01 2015

Status

approved