A115907 -id:A115907 - cp's OEIS frontend

A115904 Numbers k such that k + sigma(k) is a triangular number.

7, 10, 66, 136, 145, 196, 198, 234, 270, 438, 495, 528, 592, 606, 855, 910, 1045, 1158, 1428, 2208, 2718, 2922, 3016, 3663, 3808, 3916, 4506, 4975, 5043, 5136, 5598, 6366, 6600, 7080, 7498, 7821, 8172, 8200, 8217, 8814, 9318, 9730, 9738

Offset: 1

Giovanni Resta, Feb 06 2006

nonn

			234 + sigma(234) = 780 = T(39).

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A069066, A115907, A115909.

trnoQ[n_]:=IntegerQ[(Sqrt[1+8n]-1)/2]; Select[Range[10000], trnoQ[#+ DivisorSigma[ 1,#]]&] (* Harvey P. Dale, Apr 26 2014 *)

isok(n) = ispolygonal(n + sigma(n), 3); \\ Michel Marcus, Jan 25 2014

A115908 Numbers k such that phi(k) + prime(k) is a triangular number.

Original entry on oeis.org

1, 5, 6, 15, 23, 141, 150, 258, 317, 340, 359, 378, 471, 503, 768, 1363, 2175, 2516, 3285, 3342, 3815, 3905, 4385, 4748, 5385, 5976, 6026, 6900, 7048, 7151, 7411, 7698, 8251, 8310, 8828, 10182, 10461, 12022, 12508, 13722, 13840, 15456, 16582

Offset: 1

Giovanni Resta, Feb 06 2006

nonn

			phi(503) + prime(503) = 4095 = T(90).

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A000010, A115882, A115907.

With[{trnos = Accumulate[Range[5000]]}, Select[Range[20000], MemberQ[trnos, (EulerPhi[#] + Prime[#])] &]] (* Harvey P. Dale, Jan 12 2011 *)
Select[Range[20000],OddQ[Sqrt[8(EulerPhi[#]+Prime[#])+1]]&] (* Harvey P. Dale, Dec 08 2024 *)

isok(n) = ispolygonal(prime(n) + eulerphi(n), 3); \\ Michel Marcus, Jan 25 2014

cp's OEIS Frontend

A115904 Numbers k such that k + sigma(k) is a triangular number.

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