A365295 a(n) is the least positive integer that can be expressed as the sum of two distinct perfect powers (A001597) in exactly n ways.

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

Offset: 0

Author

Ilya Gutkovskiy, Aug 31 2023

Keywords

• nonn

Examples

			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
		

Links

• Karl-Heinz Hofmann and Hugo Pfoertner, Table of n, a(n) for n = 0..77
• Karl-Heinz Hofmann, Python program
• Hugo Pfoertner, PARI program and results (terms < 2*10^9), Sep 10 2023.

Crossrefs

Cf. A001597, A093195, A362424, A363040.

Programs

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

Extensions

a(8)-a(10) from David Consiglio, Jr., Sep 08 2023

a(9) corrected and a(11)-a(34) from Hugo Pfoertner, Sep 10 2023