id:A139141 - OEIS Search Results

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For n>=1, a(n) = floor[(d(p(n)+1) + d(p(n)+2) + d(p(n)+3) +...+d(p(n+1)))/(p(n+1)-p(n))], where d(m) is the number of positive divisors of m and p(n) is the nth prime. a(0) = floor[(d(1) + d(2))/2].

+0
2

1, 2, 2, 3, 3, 4, 3, 4, 4, 4, 5, 4, 4, 5, 4, 5, 5, 7, 5, 5, 7, 5, 5, 5, 6, 5, 5, 5, 7, 6, 5, 5, 6, 5, 6, 7, 6, 6, 5, 6, 5, 10, 6, 8, 5, 7, 6, 6, 6, 7, 6, 6, 11, 5, 7, 6, 6, 9, 7, 7, 5, 6, 7, 6, 9, 6, 7, 7, 6, 7, 8, 5, 7, 7, 7, 5, 7, 8, 7, 7, 6, 13, 6, 11, 6, 8, 6, 7, 6, 9, 6, 7, 8, 6, 7, 5, 8, 7, 7, 7, 7, 6, 8 (list; graph; listen)

	OFFSET	`0,2`
	COMMENT	`The sequence approximates the average number of divisors over all integers between consecutive primes.`
	LINKS	`Leroy Quet, Home Page (listed in lieu of email address)`
	FORMULA	`For n>= 1, a(n) = floor[A139140(n)/A001223(n)].`
	EXAMPLE	`The 9th prime is 23 and the 10th prime is 29. So a(9) = floor[d(24) + d(25) + d(26) + d(27) + d(28) + d(29))/6] = floor[(8 + 3 + 4 + 4 + 6 + 2)/6] = floor[27/6] = 4.`
	MAPLE	`A139141 := proc(n) if n = 0 then 1; else add(numtheory[tau](k), k=ithprime(n)+1..ithprime(n+1)) ; floor(%/(ithprime(n+1)-ithprime(n))) ; fi; end proc: seq(A139141(n), n=0..120) ; [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 24 2009]`
	CROSSREFS	`Cf. A139140.` `Sequence in context: A070241 A066412 A117119 this_sequence A122953 A128998 A137813` `Adjacent sequences: A139138 A139139 A139140 this_sequence A139142 A139143 A139144`
	KEYWORD	`nonn`
	AUTHOR	`Leroy Quet Apr 10 2008`
	EXTENSIONS	`Extended beyond a(11) by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 24 2009`

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Last modified November 22 20:51 EST 2009. Contains 167312 sequences.

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