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A365295
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a(n) is the least positive integer that can be expressed as the sum of two distinct perfect powers (A001597) in exactly n ways.
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1
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1, 5, 17, 129, 468, 1025, 2628, 12025, 32045, 27625, 138125, 430625, 204425, 160225, 2010025, 2348125, 801125, 1743625, 2082925, 4978025, 4005625, 12325625, 30525625, 73046025, 5928325, 13287625, 46437625, 45177925, 35409725, 120737825, 52073125, 66438125, 29641625, 32846125, 956974625
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OFFSET
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0,2
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LINKS
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EXAMPLE
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For n = 2: a(2) = 17 = 1^2 + 2^4 = 2^3 + 3^2.
a(6) = 2628 via 3^3 + 51^2 = 2^7 + 50^2 = 18^2 + 48^2 = 21^2 + 3^7 = 2^9 + 46^2 = 30^2 + 12^3. - David A. Corneth, Sep 09 2023
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PROG
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(PARI) upto(n) = {n = (sqrtint(n) + 1)^2; my(v = vector(n), pows = List([1]), r = -1, res = []); for(j = 2, logint(n, 2), for(i = 2, sqrtnint(n, j), listput(pows, i^j))); pows = Set(pows); for(i = 1, #pows - 1, j = i+1; c = pows[i] + pows[j]; while(c <= n, v[c]++; j++; c = pows[i] + pows[j])); for(i = 1, #v, c = v[i]+1; if(c > #res, res = concat(res, vector(c - #res, j, oo))); if(i < res[c], res[c] = i)); res} \\ David A. Corneth, Sep 08 2023
(PARI) \\ see link
(Python) # see link
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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