|
Search: id:A065146
|
|
|
| A065146 |
|
Arithmetic, geometric and harmonic means of Phi[m] and Sigma[m] are all integers. |
|
+0
3
|
|
| 1, 248, 264, 418, 477, 1485, 3080, 3135, 3596, 3828, 5396, 10098, 12648, 20026, 21318, 22152, 23374, 24882, 35074, 35343, 39105, 41656, 44660, 49938, 55154, 56536, 61344, 71145, 74613, 86304, 87087, 104931, 118296, 124605, 129504
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
LINKS
|
Harry J. Smith, Table of n, a(n) for n=1,...,500
|
|
FORMULA
|
a = (Phi[m]+Sigma[m])/2, g = Sqrt[Phi[m]*Sigma[m]], h = (2*Phi[m]*Sigma[m])/(Phi[m]+Sigma[m]) = g^2/a are integers; Phi[] = A000010(), Sigma[] = A000203().
|
|
EXAMPLE
|
m = 5396, Phi[m] = 2520,Sigma[m] = 10080,A-mean = 6300, G-mean = 5040,H-mean = 4032; 65 cases below 1 million.
|
|
MATHEMATICA
|
Do[s = EulerPhi[n]*DivisorSigma[1, n]; z = (EulerPhi[n]+DivisorSigma[1, n])/2; u = h[n]; If[IntegerQ[Sqrt[s]]&&IntegerQ[z]&&IntegerQ[u], Print[n]], {n, 1, 1000000}]
|
|
PROGRAM
|
(PARI) { n=0; for (m=1, 10^9, e=eulerphi(m); s=sigma(m); if (!issquare(e*s), next); h=(2*e*s)/(e + s); if (frac(h) != 0, next); if (frac((e + s)/2) != 0, next); write("b065146.txt", n++, " ", m); if (n==500, return) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Oct 12 2009]
|
|
CROSSREFS
|
Cf. A000010, A000203, A062354, A011257.
Sequence in context: A129133 A001243 A048901 this_sequence A064977 A068400 A109478
Adjacent sequences: A065143 A065144 A065145 this_sequence A065147 A065148 A065149
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Labos E. (labos(AT)ana.sote.hu), Oct 18 2001
|
|
|
Search completed in 0.005 seconds
|
