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A037225
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a(n) = phi(2n+1).
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19
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1, 2, 4, 6, 6, 10, 12, 8, 16, 18, 12, 22, 20, 18, 28, 30, 20, 24, 36, 24, 40, 42, 24, 46, 42, 32, 52, 40, 36, 58, 60, 36, 48, 66, 44, 70, 72, 40, 60, 78, 54, 82, 64, 56, 88, 72, 60, 72, 96, 60, 100, 102, 48, 106, 108, 72, 112, 88, 72, 96, 110, 80, 100, 126, 84, 130
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OFFSET
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0,2
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COMMENTS
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If 2*n+1 has r distinct odd prime factors, 2^r divides a(n).
Conjectures:
1) For any composite integer 2*n+1, a(n) doesn't divide 2*n.
2) For all n, a(n) is never equal to n. (End)
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LINKS
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FORMULA
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Sum_{k=0..n} a(k) ~ c * n^2, where c = 8/Pi^2 = 0.810569... (A217739). - Amiram Eldar, Nov 17 2022
G.f.: Sum_{n >= 1} phi(2*n+1)*x^(2*n+1) = Sum_{n >= 1} moebius(n)*x^(2*n-1)*(1 + x^(4*n-2))/(1 - x^(4*n-2))^2 = x + 2*x^3 + 4*x^5 + 6*x^7 + 6*x^9 + .... (End)
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MATHEMATICA
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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