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

1,2

Comments

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

Links

Table of n, a(n) for n=1..37.

Example

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

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 *)

Prog

(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

Crossrefs

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

Similar sequences: A093036, A093037, A340549, A350424.

Sequence in context: A082702 A214771 A065917 * A355771 A053624 A348198

Adjacent sequences: A355769 A355770 A355771 * A355773 A355774 A355775

Keyword

nonn,base

Author

Bernard Schott, Jul 18 2022

Extensions

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

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

Status

approved