A355772 - OEIS

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

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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.