A355772 Positions of records in A355770.

1, 3, 9, 15, 45, 105, 195, 315, 900, 1575, 2100, 3900, 6300, 18900, 25200, 27300, 31500, 44100, 81900, 220500, 245700, 333900, 409500, 491400, 573300, 600600, 1201200, 2402400, 3603600, 4804800, 7207200, 10810800, 14414400, 20420400, 21621600, 40840800, 43243200

Offset: 1

Author

Bernard Schott, Jul 18 2022

Keywords

• nonn
• base

Comments

Corresponding records are 1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 17, ...

Examples

			a(5) = 45 is in the sequence because A355770(45) = 5 is larger than any earlier value in A355770.
		

Crossrefs

Cf. A333369, A353735, A355770, A355771, A355773.

Similar sequences: A093036, A093037, A340549, A350424.

Programs

Mathematica

q[n_] := AllTrue[Tally @ IntegerDigits[n], EvenQ[Plus @@ #] &]; f[n_] := DivisorSum[n, 1 &, q[#] &]; fm = -1; s = {}; Do[If[(fn = f[n]) > fm, fm = fn; AppendTo[s, n]], {n, 1, 10^5}]; s (* Amiram Eldar, Jul 18 2022 *)

Python

from sympy import divisors
from itertools import count, islice
def c(n): s = str(n); return all(s.count(d)%2 == int(d)%2 for d in set(s))
def f(n): return sum(1 for d in divisors(n, generator=True) if c(d))
def agen(record=-1):
    for k in count(1):
        if f(k) > record: record = f(k); yield k
print(list(islice(agen(), 20))) # Michael S. Branicky, Jul 25 2022

Extensions

a(21)-a(31) from Michel Marcus, Jul 18 2022

a(32)-a(37) from Amiram Eldar, Jul 18 2022