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A341212 Numbers m such that m, m - 1, m - 2, m - 3 and m - 4 have k, 2k, 3k, 4k and 5k divisors respectively. 2
154379, 1075198, 4211518, 4700758, 4745227, 5954379, 6036043, 6330235, 6485998, 6524878, 6851227, 7846798, 8536027, 8556358, 11718598, 12100027, 12126838, 13584838, 14869379, 15320587, 16934998, 17074379, 18154379, 18904027, 19013129, 19774379, 19779995 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Numbers m such that tau(m) = tau(m - 1)/2 = tau(m - 2)/3 = tau(m - 3)/4 = tau(m - 4)/5, where tau(k) = the number of divisors of k (A000005).

Corresponding values of numbers k: 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, ...

First prime term 55414379 (= A341214(5)) of this sequence is the smallest prime p such that p, p - 1, p - 2, p - 3 and p - 4 have 2, 4, 6 , 8 and 10 divisors respectively.

LINKS

Robert G. Wilson v, Table of n, a(n) for n = 1..2590

EXAMPLE

tau(154375) = 20, tau(154376) = 16, tau(154377) = 12, tau(154378) = 8, tau(154379) = 4.

MATHEMATICA

seq[max_, n_] := Module[{d = DivisorSigma[0, Range[n]], s = {}}, Do[If[Length @ Union[d/Range[n, 1, -1]] == 1, AppendTo[s, k - 1]]; d = Join[Rest@d, {DivisorSigma[0, k]}], {k, n + 1, max}]; s]; seq[5*10^6, 5] (* Amiram Eldar, Feb 08 2021 *)

PROG

(MAGMA) [m: m in [5..10^6] | #Divisors(m - 1) eq 2*#Divisors(m) and #Divisors(m - 2) eq 3*#Divisors(m) and #Divisors(m - 3) eq 4*#Divisors(m) and #Divisors(m - 4) eq 5*#Divisors(m)]

(Python)

def tau(n): # A000005

    d, t = 1, 0

    while d*d < n:

        if n%d == 0:

            t = t+2

        d = d+1

    if d*d == n:

        t = t+1

    return t

n, a = 1, 2

while n <= 27:

    nn, t1 = 1, tau(a)

    while nn < 5 and tau(a-nn) == (nn+1)*t1:

        nn = nn+1

    if nn == 5:

        print(n, a)

        n = n+1

    a = a+1 # A.H.M. Smeets, Feb 07 2021

(PARI) isok(m) = if (m>5, my(nb=numdiv(m)); (numdiv(m-1) == 2*nb) && (numdiv(m-2) == 3*nb) && (numdiv(m-3) == 4*nb) && (numdiv(m-4) == 5*nb)); \\ Michel Marcus, Apr 01 2021

CROSSREFS

Cf. A000005, A340158, A340159, A341213, A314214.

Sequence in context: A339528 A234553 A073086 * A255040 A255033 A256951

Adjacent sequences:  A341209 A341210 A341211 * A341213 A341214 A341215

KEYWORD

nonn

AUTHOR

Jaroslav Krizek, Feb 07 2021

STATUS

approved

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Last modified August 9 10:38 EDT 2022. Contains 356021 sequences. (Running on oeis4.)