A386245 Composite numbers k such that A075255(k) is a square.

4, 6, 22, 135, 166, 444, 454, 636, 650, 854, 886, 1086, 1122, 1196, 1431, 1928, 2182, 2244, 2316, 2702, 3046, 3464, 3510, 3770, 4004, 4054, 4125, 4476, 4671, 5052, 5106, 5394, 5450, 6435, 6502, 6750, 8076, 8264, 8500, 9170, 9471, 9726, 10035, 10386, 10648, 10659, 11228, 11495, 11515, 11935, 12732

Offset

1,1

Comments

Composite numbers k such that k - sopfr(k) is a square, where sopfr(k) is the sum of prime factors of k with multiplicity.

Includes 2*p for p in A056899, but no odd semiprimes.

Is this sequence disjoint from A386246?

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(3) = 22 is a term because 22 = 2 * 11 is composite and 22 - (2 + 11) = 9 is a square.

Maple

filter:= proc(n) local t;
 if isprime(n) then return false fi;
 issqr(n - add(t[1]*t[2], t=ifactors(n)[2]))
end proc:
select(filter, [$4..20000]);

Crossrefs

Cf. A056899, A075255, A386246.

Sequence in context: A061596 A392308 A061597 * A075813 A107952 A004032

Adjacent sequences: A386242 A386243 A386244 * A386246 A386247 A386248

Keyword

nonn

Author

Will Gosnell and Robert Israel, Jul 16 2025

Status

approved