A375195 Numbers k such that A025487(k) and A025487(k+1) have an equal number of divisors.

4, 8, 15, 22, 69, 116, 122, 134, 135, 168, 208, 278, 400, 453, 538, 584, 718, 1019, 1409, 1671, 1799, 2035, 2417, 2541, 2595, 2783, 3424, 3809, 3860, 4415, 5628, 6267, 6672, 6745, 6872, 6873, 7277, 9436, 9845, 10182, 10191, 10936, 11272, 11472, 12105, 16139, 16277

Offset

1,1

Comments

Numbers k such that A146288(k) = A146288(k+1).

The corresponding values of A146288(k) are 4, 8, 12, 16, 48, 48, 96, 80, 80, ... .

The corresponding values of A025487(k) are 6, 24, 72, 210, 5400, ... (A375196).

Numbers k such that A146288(k) = A146288(k+1) = A146288(k+2) are 134, 6872, 6699401, 12421946, ... .

Links

Amiram Eldar, Table of n, a(n) for n = 1..4390

Formula

A025487(a(n)) = A375196(n).

Example

4 is a term since A146288(4) = A146288(5) = 4.

Mathematica

With[{lps = Cases[Import["https://oeis.org/A025487/b025487.txt", "Table"], {_, _}][[;; , 2]]}, Position[Differences[DivisorSigma[0, lps]], 0] // Flatten]

Prog

(Python)
from itertools import islice
from heapq import heappop, heappush
from sympy import divisor_count, factorint, prevprime, nextprime
def A375195_gen(): # generator of terms
    d, h, hset = 0, [1], {1}
    for c in count(0):
        m = heappop(h)
        e = divisor_count(m)
        if d == e:
            yield c
        ps = factorint(m)
        for p in ps:
            if p == 2 or ps[prevprime(p)]>ps[p]:
                mp = m*p
                if mp not in hset:
                    heappush(h, mp)
                    hset.add(mp)
        mp = m*nextprime(max(ps.keys(), default=1))
        if mp not in hset:
            heappush(h, mp)
            hset.add(mp)
        d = e
A375195_list = list(islice(A375195_gen(), 30)) # Chai Wah Wu, Mar 24 2026

Crossrefs

Cf. A000005, A025487, A146288, A375196.

Sequence in context: A102216 A001182 A264599 * A382682 A122247 A126255

Adjacent sequences: A375192 A375193 A375194 * A375196 A375197 A375198

Keyword

nonn

Author

Amiram Eldar, Aug 04 2024

Status

approved