A386623 Numbers k such that k - A224787(k) is a square.

1, 64, 630, 1225, 1296, 1750, 1925, 2079, 3125, 3402, 3888, 7150, 11495, 13000, 16445, 16464, 17160, 17500, 25578, 25935, 26082, 27508, 36975, 39083, 42688, 47125, 55955, 57188, 61740, 66671, 85085, 88451, 99372, 104544, 111375, 120736, 122452, 128898, 137547, 141427, 145509, 146927, 152592

Offset

1,2

Comments

Numbers k such that k is the sum of a square and the cubes of the prime factors of k, counted with multiplicity.

Except for a(1) = 1, all terms are the product of at least 4 (not necessarily distinct) primes.

a(1) = 1 and a(7) = 1925 have k - A224787(k) = 1. Are there any others? - Will Gosnell and Robert Israel, Aug 01 2025

Links

Robert Israel, Table of n, a(n) for n = 1..2511

Example

a(3) = 630 = 2 * 3^2 * 5 * 7 is a term because 630 - 2^3 - 2 * 3^3 - 5^3 - 7^3 = 100 is a square.

Maple

filter:= proc(n) local t;
   issqr(n - add(t[1]^3*t[2], t=ifactors(n)[2]))
end proc:
select(filter, [$1..10^6]);

Crossrefs

Cf. A224787, A385238, A386245, A386304, A386640.

Sequence in context: A067476 A179810 A303265 * A138332 A091083 A136950

Adjacent sequences: A386620 A386621 A386622 * A386624 A386625 A386626

Keyword

nonn

Author

Will Gosnell and Robert Israel, Jul 27 2025

Status

approved