A349724 Numbers k >= 1 such that A000217(k) divided by A018804(k) is an integer.

1, 2, 24, 25, 77, 153, 729, 1183, 1875, 6174, 7502, 14819, 15066, 18225, 19683, 21384, 26411, 26624, 28160, 37179, 146334, 155000, 157464, 194579, 236313, 336091, 399854, 418950, 632709, 701519, 818741, 1572864, 1605632, 2001824, 2067624, 2142075, 3670016, 3746287

Offset: 1

Author

Ctibor O. Zizka, Nov 27 2021

Keywords

• nonn

Examples

			k = 24: A000217(24) = 300, A018804(24) = 100, 300/100 = 3 thus 24 is a term.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..92

Crossrefs

Cf. A000217, A018804.

Programs

Mathematica

A018804[n_]:=Apply[Times,Apply[((#1-1)#2/#1+1)#1^#2&,FactorInteger[n],{1}]]; (* After Amiram Eldar in A018804 *)
upto=10^5;Reap[Do[If[Divisible[k(k+1)/2,A018804[k]],Sow[k]],{k,upto}]][[-1,-1]] (* Paolo Xausa, Aug 19 2022 *)

PARI

isok(k) = !(k*(k+1)/2 % sumdiv(k, d, k*eulerphi(d)/d)); \\ Michel Marcus, Nov 27 2021

Python

from itertools import islice, count
from sympy import factorint
from math import prod
def A349724(): # generator of terms
    for k in count(1):
        if not k*(k+1)//2 % prod(p**(e-1)*((p-1)*e+p) for p, e in factorint(k).items()):
            yield k
A349724_list = list(islice(A349724(),20)) # Chai Wah Wu, Nov 29 2021

Extensions

a(12)-a(20) from Paolo Xausa, Nov 27 2021

More terms from Amiram Eldar, Nov 27 2021