A359847 Oblong numbers k for which phi(k) is also an oblong number.

6, 42, 182, 650, 930, 4830, 7482, 9506, 12882, 13572, 16770, 79242, 167690, 181902, 228006, 289982, 380072, 3480090, 5209806, 6872262, 10102862, 16068072, 56002772, 56648202, 59174556, 70299840, 74831150, 123287712, 261517412, 342601590, 356322252, 455459622, 536223492, 1057452842

Offset

1,1

Comments

Since k and k+1 are relatively prime, the calculation of phi(k)*phi(k+1) is faster than that of phi(k*(k+1)). - Robert G. Wilson v, Feb 14 2023

Links

Robert G. Wilson v, Table of n, a(n) for n = 1..269

Eric Weisstein's World of Mathematics, Totient Function.

Example

9506 is a term because 9506 = 97*98 and phi(9506) = 4032 = 63*64.

Maple

lastv:= 1: R:= NULL: count:= 0:
for n from 3 while count < 50 do
  v:= numtheory:-phi(n);
  if issqr(4*v*lastv+1) then
    R:= R, n*(n-1); count:= count+1;
    fi;
  lastv:= v;
od:
R; # Robert Israel, Feb 15 2023

Mathematica

Select[Table[n*(n + 1), {n, 1, 100000}], IntegerQ @ Sqrt[4*EulerPhi[#] + 1] &] (* Amiram Eldar, Jan 15 2023 *)
k = pk0 = pk1 = 1; lst = {}; While[k < 10000, If[ IntegerQ@ Sqrt[4*pk0*pk1 + 1], AppendTo[lst, k (k + 1)]]; k++; pk0 = pk1; pk1 = EulerPhi[k + 1]]; lst (* Robert G. Wilson v, Feb 14 2023 *)

Prog

(PARI) for(k=1, 10^5, my(n=k*(k+1), p=eulerphi(n)); if(issquare(4*p+1), print1(n, ", ")))

Crossrefs

Cf. A000010, A002378, A287472.

Intersection of A002378 and A236386.

Sequence in context: A082986 A180806 A253946 * A062136 A047663 A326744

Adjacent sequences: A359844 A359845 A359846 * A359848 A359849 A359850

Keyword

nonn

Author

Alexandru Petrescu, Jan 15 2023

Status

approved