A222711 Numbers k such that gcd(sigma(k), phi(k)) (A009223) attains record values.
1, 3, 12, 14, 15, 35, 105, 190, 248, 357, 616, 812, 1045, 3080, 3135, 3339, 4064, 5049, 8323, 8636, 10659, 12441, 16065, 19780, 20026, 23374, 24871, 29029, 50065, 58435, 64285, 87685, 124355, 132957, 137885, 140335, 248501, 263055, 317205, 353133, 423657, 596037, 655707, 734517, 894387
Offset: 1
Links
- Donovan Johnson, Table of n, a(n) for n = 1..500
- N. J. A. Sloane, Transforms (The RECORDS transform returns both the high-water marks and the places where they occur).
Programs
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Mathematica
a[1] = 1; record = 1; a[n_] := a[n] = For[k = a[n-1] + 1, True, k++, g = GCD[DivisorSigma[1, k], EulerPhi[k]]; If[g > record, record = g; Return[k]]]; Table[a[n], {n, 1, 45}] (* Jean-François Alcover, Oct 07 2013 *) DeleteDuplicates[Table[{k,GCD[DivisorSigma[1,k],EulerPhi[k]]},{k,900000}],GreaterEqual[ #1[[2]],#2[[2]]]&][[;;,1]] (* Harvey P. Dale, Jun 22 2024 *) -
PARI
mg=0;for(x=1,1000000,g=A009223(x);if(g>mg,print1(x", ");mg=g))
Comments