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A065550
a(n) = floor(sqrt(phi(w)*sigma(w)+w^2)), where w=10^n.
0
13, 136, 1391, 14030, 140865, 1411444, 14128309, 141352267, 1413868217, 14140409111, 141412724154, 1414170403052, 14141919829640, 141420277272713, 1414208167563878, 14142108649717545, 141421221367320690, 1414212888023339560, 14142132251982630599, 141421339378569021517
OFFSET
1,1
COMMENTS
a(n) tends to sqrt(2)*(10^n) when n->oo.
FORMULA
a(n) = floor(sqrt(A062354(w) + A000290(w))), where w=10^n.
MATHEMATICA
a[n_] := Floor[Sqrt[EulerPhi[10^n] * DivisorSigma[1, 10^n] + 100^n]]; Array[a, 20] (* Amiram Eldar, Jun 12 2022 *)
PROG
(PARI) a(n) = my(w=10^n); sqrtint(eulerphi(w)*sigma(w)+w^2); \\ Michel Marcus, Mar 23 2020
(Python)
from sympy import integer_nthroot, totient as phi, divisor_sigma as sigma
def isqrt(n): return integer_nthroot(n, 2)[0]
def a(n): w = 10**n; return isqrt(phi(w)*sigma(w, 1) + w**2)
print([a(n) for n in range(1, 21)]) # Michael S. Branicky, Jun 12 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Nov 13 2001
EXTENSIONS
Corrected and extended by Michel Marcus, Jun 12 2022
STATUS
approved