A075434 -id:A075434 - cp's OEIS frontend

A085253 Numbers having no representation as sum of two powerful numbers (A001694).

1, 3, 4, 6, 7, 11, 14, 15, 19, 21, 22, 23, 27, 30, 38, 39, 42, 46, 47, 49, 51, 55, 56, 60, 62, 66, 67, 69, 70, 71, 75, 77, 78, 79, 83, 84, 86, 87, 92, 93, 94, 95, 102, 103, 105, 107, 110, 111, 114, 115, 118, 119, 120, 123, 131, 138, 139, 142, 143, 147, 151, 154

Offset: 1

Reinhard Zumkeller, Jun 23 2003

nonn

Complement of A076871.

Amiram Eldar, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Powerful Number.

Cf. A001694, A076871, A085252.

Different from A075434.

With[{m = 160}, pow = Select[Range[m], # == 1 || Min[FactorInteger[#][[;; , 2]]] > 1 &]; Complement[Range[m], Select[Union[Plus @@@ Tuples[pow, {2}]], # <= m &]]] (* Amiram Eldar, Jan 30 2023 *)

A085252(a(n)) = 0.

A070049 Sum of two perfect powers.

Original entry on oeis.org

2, 5, 8, 9, 10, 12, 13, 16, 17, 18, 20, 24, 25, 26, 28, 29, 31, 32, 33, 34, 35, 36, 37, 40, 41, 43, 44, 45, 48, 50, 52, 53, 54, 57, 58, 59, 61, 63, 64, 65, 68, 72, 73, 74, 76, 80, 81, 82, 85, 89, 90, 91, 96, 97, 98, 100, 101, 104, 106, 108, 109, 113, 116, 117, 122, 125

Offset: 1

Sharon Sela (sharonsela(AT)hotmail.com), May 06 2002

Cf. A001597, complement of A075434.

lista(nn) = {vec = vector(nn, i, i); pp = concat(1, select(i->ispower(i) , vec)); sumpp = Set(); for (i = 1, #pp, for (j = 1, #pp, sumpp = Set(concat(sumpp, pp[i]+pp[j])););); for (i = 1, #sumpp, if (sumpp[i] <= nn, print1(sumpp[i], ", ")););} \\ Michel Marcus, Oct 04 2013

More terms from Rick L. Shepherd, Aug 24 2002

cp's OEIS Frontend

A085253 Numbers having no representation as sum of two powerful numbers (A001694).

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