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A360356 Primitive terms of A360332: terms of A360332 with no proper divisor in A360332. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
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
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]
PROG
(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)};
CROSSREFS
Subsequence of A360332.
Cf. A320628.
Similar sequences: A006038, A091191, A249263, A302574, A360355.
Sequence in context: A280932 A039534 A360332 * A063347 A219807 A219458
KEYWORD
nonn
AUTHOR
Amiram Eldar, Feb 04 2023
STATUS
approved

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Last modified July 22 12:22 EDT 2024. Contains 374499 sequences. (Running on oeis4.)