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 A092517 Product of tau values for consecutive integers. 13
 2, 4, 6, 6, 8, 8, 8, 12, 12, 8, 12, 12, 8, 16, 20, 10, 12, 12, 12, 24, 16, 8, 16, 24, 12, 16, 24, 12, 16, 16, 12, 24, 16, 16, 36, 18, 8, 16, 32, 16, 16, 16, 12, 36, 24, 8, 20, 30, 18, 24, 24, 12, 16, 32, 32, 32, 16, 8, 24, 24, 8, 24, 42, 28, 32, 16, 12, 24, 32, 16, 24, 24, 8, 24, 36 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Number of divisors of the n-th oblong number. - Ray Chandler, Jun 23 2008 Number of positive solutions (x,y) for which n/x + (n+1)/y = 1. - Michel Lagneau, Jan 16 2014 Number of positive solutions for which 1/p + 1/q + 1/(p*q) = 1/n; set p=x and q=y-1 in the solutions (x,y) in the comment above. - Mo Li, Apr 27 2021 a(n) is the maximum number of b > 0, which allows us to write (n+1)^2 as a sum of n+1 parts. Each part is of the form b^c and c is an integer >= 0 independent for each part. For n = 2 this is 3^2 = 2^2 + 2^2 + 2^0 = 3^1 + 3^1 + 3^1 = 4^1 + 4^1 + 4^0 = 7^1 + 7^0 + 7^0, b = 2;3;4;7 and a(2) = 4. It is conjectured that for all n the number of possible b reaches a(n). - Thomas Scheuerle, Jan 12 2022 LINKS Ray Chandler, Table of n, a(n) for n = 1..10000 FORMULA a(n) = A000005(n)*A000005(n+1) = A000005(n*(n+1)) = A000005(A002378(n)) = 2*A063123(n). MAPLE with(numtheory): seq(tau(n)*tau(n+1), n=1..73); # Zerinvary Lajos, Jan 22 2007 MATHEMATICA Table[DivisorSigma[0, n^2+n], {n, 100}] (* Giorgos Kalogeropoulos, Apr 28 2021 *) Times@@#&/@Partition[DivisorSigma[0, Range[80]], 2, 1] (* Harvey P. Dale, Apr 21 2022 *) PROG (Magma) [ NumberOfDivisors(n^2+n) : n in [1..100]]; // Vincenzo Librandi, Apr 03 2011 (PARI) a(n) = numdiv(n^2+n); \\ Michel Marcus, Jan 11 2020 (Python) from sympy import divisor_count def A092517(n): return divisor_count(n)*divisor_count(n+1) # Chai Wah Wu, Jan 06 2022 CROSSREFS Cf. A000005, A002378, A063123, A063440, A083539, A123000. Sequence in context: A111973 A349787 A161655 * A128558 A090346 A267460 Adjacent sequences: A092514 A092515 A092516 * A092518 A092519 A092520 KEYWORD nonn AUTHOR Reinhard Zumkeller, Apr 06 2004 EXTENSIONS Extended by Ray Chandler, Jun 23 2008 STATUS approved

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Last modified April 1 19:13 EDT 2023. Contains 361695 sequences. (Running on oeis4.)