OFFSET
1,2
COMMENTS
A coreful divisor d of n is a divisor that is divisible by every prime that divides n (see also A307958).
Numbers k such that A372739(k) = 0.
Numbers that are not in the range of A336563.
Except for 1, all the terms are not squarefree (A013929), because if k is squarefree (A005117), and there is a prime p such that p|k, then A336563(p*k) = k.
Includes all the squares of primes (A001248).
The numbers of terms that do not exceed 10^k, for k = 1, 2, ..., are , 4, 29, 281, 2762, 27690, ... . Apparently, the asymptotic density of this sequence exists and equals 0.27... .
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
MATHEMATICA
f[p_, e_] := (p^(e + 1) - 1)/(p - 1) - 1; s[1] = 0; s[n_] := Times @@ f @@@ FactorInteger[n] - n; seq[max_] := Module[{v = Table[0, {max}], i}, Do[i = s[k]; If[0 < i <= max, v[[i]]++], {k, 1, max^2}]; Position[v, _?(# == 0 &)] // Flatten]; seq[200]
PROG
(PARI) s(n) = {my(f = factor(n)); prod(i = 1, #f~, (f[i, 1]^(f[i, 2] + 1) - 1)/(f[i, 1] - 1) - 1) - n; }
lista(nmax) = {my(v = vector(nmax), i); for(k = 1, nmax^2, i = s(k); if(i > 0 && i <= nmax, v[i]++)); for(k = 1, nmax, if(v[k] == 0, print1(k, ", "))); }
CROSSREFS
A001248 is a subsequence.
KEYWORD
nonn
AUTHOR
Amiram Eldar, May 12 2024
STATUS
approved