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A331185
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a(n) = n - prime(A067004(n)), where A067004 is the ordinal transform of number of divisors of n (A000005).
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3
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-1, 0, 0, 2, 0, 4, 0, 5, 6, 5, 0, 10, 0, 7, 4, 14, 0, 15, 0, 15, 8, 5, 0, 22, 20, 7, 4, 21, 0, 27, 0, 21, 4, 3, -2, 34, 0, -3, -4, 35, 0, 35, 0, 31, 28, -1, 0, 46, 42, 31, -2, 29, 0, 43, -4, 43, -4, -9, 0, 58, 0, -9, 34, 62, -8, 49, 0, 37, -10, 51, 0, 69, 0, -9, 38, 35, -12, 55, 0, 77, 78, -15, 0, 79, -16, -17, -20, 59, 0, 83
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OFFSET
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1,4
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LINKS
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FORMULA
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MATHEMATICA
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b[_] = 0;
c[n_] := c[n] = With[{t = DivisorSigma[0, n]}, b[t] = b[t]+1];
a[n_] := n - Prime[c[n]];
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PROG
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(PARI)
up_to = 65537;
ordinal_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), pt); for(i=1, length(invec), if(mapisdefined(om, invec[i]), pt = mapget(om, invec[i]), pt = 0); outvec[i] = (1+pt); mapput(om, invec[i], (1+pt))); outvec; };
v067004 = ordinal_transform(vector(up_to, n, numdiv(n)));
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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