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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.)