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

Author

Alexandru Petrescu, Jan 15 2023

Keywords

• nonn

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

Examples

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

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..269
• Eric Weisstein's World of Mathematics, Totient Function.

Crossrefs

Cf. A000010, A002378, A287472.

Intersection of A002378 and A236386.

Programs

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 *)

PARI

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