A340157 - OEIS

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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.

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)), 2tau(a(n)), 3tau(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 August 12 23:52 EDT 2022. Contains 356077 sequences. (Running on oeis4.)