A386954 Numbers k such that A075255(k) is the square of a prime.

22, 135, 1431, 1928, 2244, 3510, 3770, 4671, 5106, 5394, 5450, 9471, 10648, 10659, 11495, 11515, 11935, 17451, 22253, 22311, 24725, 26724, 26994, 27965, 36580, 37350, 37863, 38691, 40311, 50034, 50888, 51651, 52546, 54417, 54730, 55090, 58179, 58386, 59031, 63085, 65288, 72008, 72580, 72770

Offset

1,1

Comments

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

Links

Robert Israel, Table of n, a(n) for n = 1..5300

Example

a(3) = 1431 is a term because 1431 = 3^3 * 53 and 1431 - (3*3 + 53) = 1369 = 37^2, and 37 is a prime.

Maple

sopfr:= proc(n) local F, t;
  F:= ifactors(n)[2];
  add(t[1]*t[2], t=F)
end proc:
filter:= proc(n) local k;
k:= n - sopfr(n);
issqr(k) and isprime(sqrt(k))
end proc:
select(filter, [$4..10^5]);

Mathematica

lim=10^5; s=Join[{1}, Table[n - Total[Times@@@FactorInteger[n]], {n, 2, lim}]] ; Select[Range[lim], PrimeQ[Sqrt[s[[#]]]]&] (* James C. McMahon, Sep 15 2025 *)

Crossrefs

Cf. A075255. Subset of A386245.

Sequence in context: A041936 A254699 A391667 * A183909 A263481 A238170

Adjacent sequences: A386951 A386952 A386953 * A386955 A386956 A386957

Keyword

nonn

Author

Will Gosnell and Robert Israel, Sep 13 2025

Status

approved