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A353217
Triangular numbers (A000217) with arithmetic derivative (A003415) a palindrome (A002113).
0
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
1,3
EXAMPLE
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.
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 *)
PROG
(Magma) tr:=func<m|IsSquare(8*m+1)>; pal:=func<n|Intseq(n) eq Reverse(Intseq(n))>; f:=func<n |n le 1 select 0 else n*(&+[Factorisation(n)[i][2] / Factorisation(n)[i][1]: i in [1..#Factorisation(n)]])>; [n:n in [d*(d+1) div 2:d in [0..150000]]| pal(Floor(f(n)))];
(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
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Marius A. Burtea, Apr 30 2022
STATUS
approved