A353217 Triangular numbers (A000217) with arithmetic derivative (A003415) a palindrome (A002113).

0, 1, 3, 6, 10, 15, 136, 153, 231, 741, 1711, 11026, 22366, 99681, 104653, 593505, 1348903, 1378630, 1886653, 3098805, 4388203, 4474536, 24587578, 26626753, 32092066, 45825951, 132804253, 165283471, 197239591, 355657785, 498727153, 866008153, 1074091726, 1144165366

Offset: 1

Author

Marius A. Burtea, Apr 30 2022

Keywords

• nonn
• base

Examples

			15 = A000217(5) and 15' = 8 = A002113(9), so 15 is a term.
153 = A000217(17) and 153' = 111 = A002113(21), so 153 is a term.
		

Crossrefs

Cf. A000217, A003415, A002113, A068312.

Programs

Magma

tr:=func; pal:=func; f:=func; [n:n in [d*(d+1) div 2:d in [0..150000]]| pal(Floor(f(n)))];

Mathematica

d[0] = d[1] = 0; d[n_] := n*Plus @@ ((Last[#]/First[#]) & /@ FactorInteger[n]); Select[Table[n*(n + 1)/2, {n, 0, 50000}], PalindromeQ[d[#]] &] (* Amiram Eldar, Apr 30 2022 *)

Python

from itertools import chain, count, islice
from sympy import factorint
def A353217_gen(): # generator of terms
    return chain((0,1),filter(lambda m:(s:=str(sum((m*e//p for p,e in factorint(m).items()))))[:(t:=(len(s)+1)//2)]==s[:-t-1:-1],(n*(n+1)//2 for n in count(2))))
A353217_list = list(islice(A353217_gen(),20)) # Chai Wah Wu, Jun 24 2022