A360356 Primitive terms of A360332: terms of A360332 with no proper divisor in A360332.

56, 104, 196, 304, 364, 368, 464, 532, 644, 812, 1036, 1184, 1204, 1316, 1376, 1484, 1504, 1696, 1708, 1952, 1988, 2044, 2212, 2492, 2716, 2828, 2884, 2996, 3164, 3496, 3668, 3836, 3892, 4172, 4228, 4408, 4544, 4564, 4672, 4676, 4844, 5056, 5068, 5336, 5404, 5516

Offset: 1

Author

Amiram Eldar, Feb 04 2023

Keywords

• nonn

Comments

If m is a term then k*m is a term of A360332 for all k in A320628.

Analogous to primitive abundant numbers (A091191) with divisors that are restricted to numbers that have only nonprime-indexed prime factors.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Subsequence of A360332.

Cf. A320628.

Similar sequences: A006038, A091191, A249263, A302574, A360355.

Programs

Mathematica

f[p_, e_] := If[PrimeQ[PrimePi[p]], 1, (p^(e + 1) - 1)/(p - 1)]; s[1] = 1; s[n_] := Times @@ f @@@ FactorInteger[n]; primQ[n_] := s[n] > 2*n && AllTrue[Divisors[n], # == n || s[#] <= 2*# &]; Select[Range[6000], primQ]

PARI

isab(n) = {my(f = factor(n), p = f[,1], e = f[,2]); prod(i = 1, #p, if(isprime(primepi(p[i])), 1, (p[i]^(e[i]+1)-1)/(p[i]-1))) > 2*n;}
is(n) = {if(!isab(n), return(0)); fordiv(n, d, if(d < n && isab(d), return(0))); return(1)};