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 A340157 Numbers m such that numbers m, m + 1, m + 2 and m + 3 have k, 2k, 3k and 4k divisors respectively. 3
 421, 3013, 5029, 5223, 5245, 5893, 6487, 10533, 11911, 14677, 17173, 23077, 23573, 24613, 25141, 25213, 27637, 27973, 28357, 30661, 32407, 34117, 37477, 38282, 39751, 43495, 45973, 47365, 48423, 50821, 50965, 53413, 53989, 54421, 55141, 56103, 57877, 58165 (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, where tau(k) = the number of divisors of k (A000005). Quadruplets of [tau(a(n)), tau(a(n) + 1), tau(a(n) + 2), tau(a(n) + 3)] = [tau(a(n)), 2*tau(a(n)), 3*tau(a(n)), 4*tau(a(n))]: [2, 4, 6, 8], [4, 8, 12, 16], [4, 8, 12, 16], [4, 8, 12, 16], [4, 8, 12, 16], [4, 8, 12, 16], [4, 8, 12, 16], ... Corresponding values of tau(a(n)): 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, ... Subsequence of A063446 and A339778. Supersequence of A340158. Prime terms (primes p such that p, p + 1, p + 2 and p + 3 have 2, 4, 6 and 8 divisors respectively): 421, 30661, 50821, 54421, 130021, 195541, 423781, 635461, 1003381, 1577941, 1597381, 1883941, ... LINKS Table of n, a(n) for n=1..38. EXAMPLE tau(421) = 2, tau(422) = 4, tau(423) = 6, tau(424) = 8. MATHEMATICA Select[Range[60000], Equal @@ (DivisorSigma[0, # + {0, 1, 2, 3}]/{1, 2, 3, 4}) &] (* Amiram Eldar, Dec 30 2020 *) PROG (Magma) [m: m in [1..10^5] | #Divisors(m) eq #Divisors(m + 1)/2 and #Divisors(m) eq #Divisors(m + 2)/3 and #Divisors(m) eq #Divisors(m + 3)/4] (PARI) isok(m, n=4) = {my(k=numdiv(m)); for (i=1, n-1, if (numdiv(m+i) != (i+1)*k, return (0)); ); return(1); } \\ Michel Marcus, Dec 30 2020 CROSSREFS Cf. A000005, A063446, A294528, A303578, A339778, A340158, A340159. Sequence in context: A142853 A217587 A068701 * A302284 A353045 A302732 Adjacent sequences: A340154 A340155 A340156 * A340158 A340159 A340160 KEYWORD nonn AUTHOR Jaroslav Krizek, Dec 29 2020 STATUS approved

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Last modified September 11 23:47 EDT 2024. Contains 375842 sequences. (Running on oeis4.)