A053140 Odd primes that are not highly-imperfect numbers.

181, 241, 251, 257, 263, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653

Offset: 1

Author

Joseph L. Pe, Oct 03 2002

Keywords

• nonn

Comments

The sequence of highly-imperfect numbers begins with 1 and the odd primes up to 113... then even numbers appear and some odd primes are left out.

Links

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

Crossrefs

Cf. A074918.

Programs

Maple

R:= NULL: count:= 0: m:= 0: q:= 1:
for k from 1 do
  v:= abs(numtheory:-sigma(k)-2*k);
  if v > m then
    m:= v;
    V:= select(isprime,[seq(i,i=q .. k-1,2)]);
    count:= count + nops(V);
    R:= R, op(V);
    q:= k + 1 + (k mod 2);
    if count > 100 then break fi
  fi
od:
R; # Robert Israel, Jun 19 2025

Extensions

More terms from Sean A. Irvine, Dec 11 2021