login
A349724
Numbers k >= 1 such that A000217(k) divided by A018804(k) is an integer.
1
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
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
Sequence in context: A258781 A371207 A064818 * A022374 A139334 A212759
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