A115908 -id:A115908 - cp's OEIS frontend

A115905 Numbers k such that k + phi(k) is a triangular number.

2, 4, 9, 11, 20, 23, 25, 27, 49, 53, 92, 93, 105, 121, 127, 147, 150, 163, 169, 220, 228, 231, 233, 281, 286, 289, 294, 332, 361, 431, 474, 529, 541, 543, 548, 613, 660, 675, 710, 726, 743, 825, 827, 841, 888, 891, 961, 977, 993, 1014, 1028, 1265, 1310, 1369

Offset: 1

Giovanni Resta, Feb 06 2006

nonn

			121 + phi(121) = 231 = T(21).

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

Cf. A000010, A000217, A069066, A115908, A115910.

Select[Range[1500],OddQ[Sqrt[8(#+EulerPhi[#])+1]]&] (* Harvey P. Dale, May 11 2015 *)

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

A115907 Numbers k such that sigma(k) plus the k-th prime is a triangular number.

Original entry on oeis.org

1, 2, 9, 13, 21, 80, 112, 129, 147, 225, 308, 349, 1063, 1282, 1300, 1635, 1880, 2686, 2956, 3517, 3759, 3907, 4058, 5025, 5196, 6742, 7606, 7708, 9244, 10154, 10596, 11259, 11719, 12687, 13167, 13599, 14081, 14624, 15937, 16437, 16766, 18289

Offset: 1

Giovanni Resta, Feb 06 2006

nonn

			sigma(1880) + prime(1880) = 20503 = T(202).

David A. Corneth, Table of n, a(n) for n = 1..11241 (first 1000 from Robert Israel)

Cf. A000040, A000203, A000217, A115882, A115908.

filter:= n -> issqr(1+8*(numtheory:-sigma(n)+ithprime(n))):
select(filter, [$1..10^5]); # Robert Israel, Nov 07 2018

Select[Range[25000],IntegerQ[(Sqrt[8(DivisorSigma[1,#]+Prime[#])+ 1]-1)/2]&] (* Harvey P. Dale, Jun 07 2011 *)

upto(n) = my(t = 0, res = List(), u = prime(n)); forprime(p = 2, u, t++; c = p + sigma(t); if(ispolygonal(c, 3), listput(res, t))); res \\ David A. Corneth, Nov 08 2018

cp's OEIS Frontend

A115905 Numbers k such that k + phi(k) is a triangular number.

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