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

1,2

Links

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A000217, A018804.

Sequence in context: A258781 A371207 A064818 * A022374 A139334 A212759

Adjacent sequences: A349721 A349722 A349723 * A349725 A349726 A349727

Keyword

nonn

Author

Ctibor O. Zizka, Nov 27 2021

Extensions

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

More terms from Amiram Eldar, Nov 27 2021

Status

approved