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 A177431 a(n) = sqrt(A177430(n)) where A177430 is the least monotonically increasing logarithmic derivative consisting of only squares. 2
 1, 3, 4, 5, 6, 12, 13, 15, 22, 28, 32, 34, 38, 39, 51, 55, 67, 72, 75, 80, 88, 96, 114, 126, 131, 140, 157, 159, 173, 187, 216, 217, 224, 235, 237, 250, 258, 263, 269, 280, 286, 306, 343, 346, 348, 388, 422, 430, 454, 497, 506, 512, 529, 531, 533, 545, 555, 577 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Conjecture: the series exp(Sum_{n>=1} a(n)^m*x^n/n) consists entirely of integer coefficients only when m is a nonnegative even integer. LINKS FORMULA a(n) = sqrt( A177430(n) ). EXAMPLE L.g.f.: L(x) = x + 9*x^2/2 + 16*x^3/3 + 25*x^4/4 + 36*x^5/5 +...+ a(n)^2*x^n/n +... exp(L(x)) = 1 + x + 5*x^2 + 10*x^3 + 24*x^4 + 51*x^5 + 122*x^6 + 244*x^7 +...+ A177432(n)*x^n +... PROG (PARI) {a(n)=local(V, A=[1], M); V=Vec(exp(x+sum(k=2, n-1, a(k)^2*x^k/k)+t*x^n/n+x*O(x^n))); if(n==1, M=1, M=a(n-1); for(m=M+1, 3*M, if(denominator(subst(V[ #V], t, m^2))==1, M=m^2; break)); sqrtint(M))} CROSSREFS Cf. A177430, A177432. Sequence in context: A125139 A107224 A026493 * A145735 A213206 A070981 Adjacent sequences:  A177428 A177429 A177430 * A177432 A177433 A177434 KEYWORD nonn AUTHOR Paul D. Hanna, Sep 06 2010 STATUS approved

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