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A035166
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Let d(n) = denominator of Sum_{k=1..n} 1/k^2 and consider f(n) = product of primes which appear to odd powers in d(n); sequence lists n such that f(n) is different from f(n-1).
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0
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1, 10, 15, 20, 25, 42, 49, 50, 55, 66, 75, 78, 91, 100, 110, 121, 125, 136, 153, 156, 164, 169, 171, 182, 189, 190, 205, 250, 253, 272, 276, 289, 294, 342, 343, 354, 361, 375, 406, 413, 435, 465, 473, 496, 500, 506, 516, 529, 555, 592, 605, 625
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| The prime 479 first appears in 2395, ahead of 71, which first appears at 2485. The first occurrence of four distinct primes is at 2500, with 5^7 17^3, 17 and 479. For 1890<n<2006, d(n) is square (f(n)=1). The lone prime in 1875-1890 is 61 and in 2006-2027 it is 59. It appears that adjacent years can differ in at most one prime.
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EXAMPLE
| f(10) = 5 is the first time f(n) > 1. The 5 persists until n reaches 15 when it disappears.
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PROG
| (MACSYMA) for k:1 do (subset(factor_number(denom(harmonic(k, 2))), lambda([x], oddp(second(x)))), if old#old:%% then print(k, %%))
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CROSSREFS
| Cf. A075326, A075327, A007407.
Sequence in context: A138593 A004259 A006623 * A129495 A101258 A091418
Adjacent sequences: A035163 A035164 A035165 * A035167 A035168 A035169
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KEYWORD
| nonn,nice
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AUTHOR
| R. W. Gosper Sep 04 2002
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