A259496 Numbers n such that phi(n) + d(n) = phi(n+1) + d(n+1), where phi(n) is the Euler totient function of n and d(n) the number of divisors of n.

5, 7, 104, 105, 1754, 3255, 16215, 22935, 67431, 93074, 983775, 1025504, 2200694, 2619705, 3365438, 4163355, 4447064, 4695704, 6372794, 7838265, 9718904, 11903775, 23992215, 26879684, 29357475, 37239735, 40588485, 41207144, 48615735, 56424555, 76466985, 81591194, 83864055

Offset

1,1

Comments

So far, less than 10^9, except for 7, 67431 & 3365438, all terms have been congruent to 5 or 4 (mod 10). - Robert G. Wilson v, Jul 06 2015

Links

Giovanni Resta, Table of n, a(n) for n = 1..600 (first 65 terms from Robert G. Wilson v)

Example

phi(5) + d(5) = 4 + 2 = 6 and phi(6) + d(6) = 2 + 4 = 6.
phi(7) + d(7) = 6 + 2 = 8 and phi(8) + d(8) = 4 + 4 = 8.

Maple

with(numtheory): P:=proc(q) local n; for n from 1 to q do
if phi(n)+tau(n)=phi(n+1)+tau(n+1) then print(n); fi;
od; end: P(10^9);

Mathematica

a = k = 2; lst = {}; While[k < 100000001, b = EulerPhi[k] + DivisorSigma[0, k]; If[a == b, AppendTo[lst, k - 1]]; k++; a = b]; lst

Prog

(Magma) [n: n in [1..6*10^6] | EulerPhi(n) + NumberOfDivisors(n) eq EulerPhi(n+1) + NumberOfDivisors(n+1)]; // Vincenzo Librandi, Jun 30 2015

Crossrefs

Cf. A000005, A000010, A061468, A054004, A145749, A259495.

Sequence in context: A230379 A292847 A088270 * A338525 A267586 A224507

Adjacent sequences: A259493 A259494 A259495 * A259497 A259498 A259499

Keyword

nonn

Author

Paolo P. Lava, Jun 29 2015

Extensions

a(23)-a(33) from Robert G. Wilson v, Jul 05 2015

Status

approved