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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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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; refs; listen; history; internal format)
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OFFSET
| 0,2
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REFERENCES
| J. W. L. Glaisher, On the square of Euler's series, Proc. London Math. Soc., 21 (1889), 182-194.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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FORMULA
| 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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PROG
| (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
| a(n)=A002654(12n+1)=A121363(3n).
Sequence in context: A026490 A053555 A124160 * A170823 A068073 A032452
Adjacent sequences: A002172 A002173 A002174 * A002176 A002177 A002178
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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