A390154 Numbers k such that k^2 is the difference of j and the sum of its prime factors (counted with multiplicity) for some j.

0, 1, 3, 9, 11, 15, 20, 21, 24, 25, 28, 30, 33, 34, 37, 39, 41, 45, 46, 47, 50, 55, 57, 59, 61, 63, 64, 67, 68, 71, 73, 80, 81, 82, 85, 86, 90, 92, 95, 97, 99, 103, 104, 105, 107, 108, 109, 111, 115, 117, 118, 119, 123, 128, 131, 135, 141, 143, 145, 147, 148, 149, 153, 155, 156, 157, 158, 160, 163

Offset

1,3

Comments

Numbers k such that k^2 = A075255(j) for some j.

Links

Robert Israel, Table of n, a(n) for n = 1..2175

Example

a(5) = 11 is a term because 135 = 3^3 * 5 and 135 - 3*3 - 5 = 121 = 11^2.

Maple

S:= {}:
for n from 1 to 50000 do
  if isprime(n) then next fi;
  v:= n - add(t[1]*t[2], t=ifactors(n)[2]);
  if v <= 25000 and issqr(v) then S:= S union {sqrt(v)} fi
od:
sort(convert(S, list));

Crossrefs

Cf. A075255, A386245, A390150.

Sequence in context: A059326 A370873 A028312 * A310315 A074486 A131861

Adjacent sequences: A390151 A390152 A390153 * A390155 A390156 A390157

Keyword

nonn

Author

Will Gosnell and Robert Israel, Oct 27 2025

Status

approved