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A353813
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a(n) = 1 if n has exactly one prime factor of form 4*k+1 (when counted with multiplicity) and no prime factor 4*k+3 with odd multiplicity, otherwise 0.
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5
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0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0
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OFFSET
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1
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LINKS
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FORMULA
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a(n) = [A004018(n) == 8], where [ ] is the Iverson bracket.
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PROG
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(PARI) A353813(n) = { my(f = factor(n), nb1 = 0, p, ep); for(i=1, #f~, p = f[i, 1]; ep = f[i, 2]; if(1==(p%4), nb1++; if((ep>1)||(nb1>1), return(0))); if((3==(p%4)) && (ep%2), return(0))); return(1==nb1); }; \\ After "isok" function in A230779
(PARI)
A004018(n) = if(n<1, n==0, 4 * sumdiv( n, d, (d%4==1) - (d%4==3))); \\ From A004018
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CROSSREFS
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Characteristic function of A230779.
Differs from A353812 for the first time at n=325, where a(325) = 0, while A353812(325) = 1.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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