A308664
Numbers k such that tau(k) and phi(k) are the legs of a Pythagorean triple.
Original entry on oeis.org
20, 36, 60, 100, 300
Offset: 1
60 is in this sequence because tau(60) = 12 and phi(60) = 16, legs of the Pythagorean triple {12, 16, 20} (12^2 + 16^2 = 20^2).
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Select[Range[300], IntegerQ@Sqrt[DivisorSigma[0, #]^2 + EulerPhi[#]^2] &] (* Amiram Eldar, Jul 26 2019 *)
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for(i = 1, 2000, a = eulerphi(i); b = numdiv(i); if(issquare(a^2 + b^2), print1(i,", ")))
A378089
Irregular triangle read by rows in which row n lists the numbers k such that phi(k)/tau(k) = n.
Original entry on oeis.org
1, 3, 8, 10, 18, 24, 30, 5, 9, 15, 28, 40, 72, 84, 90, 120, 7, 21, 26, 56, 70, 78, 108, 126, 168, 210, 34, 45, 52, 102, 140, 156, 252, 360, 420, 11, 33, 88, 110, 198, 264, 330, 13, 35, 39, 63, 76, 104, 105, 130, 228, 234, 280, 312, 390, 504, 540, 630, 840, 58, 98, 174, 294
Offset: 1
Triangle begins:
n=1: 1, 3, 8, 10, 18, 24, 30;
n=2: 5, 9, 15, 28, 40, 72, 84, 90, 120;
n=3: 7, 21, 26, 56, 70, 78, 108, 126, 168, 210;
n=4: 34, 45, 52, 102, 140, 156, 252, 360, 420;
n=5: 11, 33, 88, 110, 198, 264, 330;
n=6: 13, 35, 39, 63, 76, 104, 105, 130, 228, 234, 280, 312, 390, 504, 540, 630, 840;
n=7: 58, 98, 174, 294;
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