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Search: id:A002175
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| A002175 |
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Excess of number of divisors of 12n+1 of form 4k+1 over those of form 4k+3.
(Formerly M0416 N0159)
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+0
7
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| 1, 2, 3, 2, 1, 2, 2, 4, 2, 2, 1, 0, 4, 2, 3, 2, 2, 4, 0, 2, 2, 0, 4, 2, 3, 0, 2, 6, 2, 2, 1, 2, 0, 2, 2, 2, 2, 4, 2, 0, 4, 4, 4, 0, 1, 2, 0, 4, 2, 0, 2, 2, 5, 2, 0, 2, 2, 4, 4, 2, 0, 2, 4, 2, 2, 0, 4, 0, 0, 2, 3, 2, 4, 2, 0, 4, 0, 6, 2, 4, 1, 0, 4, 2, 2, 2, 2, 0, 0, 2, 0, 2, 8, 2, 2, 0, 2, 4, 0, 4, 2, 2, 3, 2, 2
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
J. W. L. Glaisher, On the square of Euler's series, Proc. London Math. Soc., 21 (1889), 182-194.
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FORMULA
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Expansion of q^(-1/12)(eta(q^2)eta(q^3)^2/(eta(q)eta(q^6)))^2 in powers of q.
Euler transform of period 6 sequence [2, 0, -2, 0, 2, -2, ...]. - Michael Somos Sep 19 2005
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PROGRAM
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(PARI) {a(n)=if(n<0, 0, n=12*n+1; sumdiv(n, d, (d%4==1)-(d%4==3)))}
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CROSSREFS
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a(n)=A002654(12n+1)=A121363(3n).
Sequence in context: A026490 A053555 A124160 this_sequence A068073 A032452 A084199
Adjacent sequences: A002172 A002173 A002174 this_sequence A002176 A002177 A002178
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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