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A360355 Primitive terms of A360328: terms of A360328 with no proper divisor in A360328. 1
7425, 8415, 46035, 76725, 101475, 182655, 355725, 669735, 1411425, 1606275, 2352375, 2891295, 3592215, 3650625, 4079295, 4861575, 5053455, 5870205, 6093225, 6636465, 6920595, 7732395, 8750835, 9120375, 9783675, 9850005, 9958905, 10155375, 11298375, 11532375, 12120075 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
If m is a term then k*m is a term of A360328 for all k in A076610.
Analogous to primitive abundant numbers (A091191) with divisors that are restricted to numbers that have only prime-indexed prime factors.
LINKS
MATHEMATICA
f[p_, e_] := If[PrimeQ[PrimePi[p]], (p^(e + 1) - 1)/(p - 1), 1]; s[1] = 1; s[n_] := Times @@ f @@@ FactorInteger[n]; primQ[n_] := s[n] > 2*n && AllTrue[Divisors[n], # == n || s[#] <= 2*# &]; Select[Range[10^6], primQ]
PROG
(PARI) isab(n) = {my(f = factor(n), p = f[, 1], e = f[, 2]); prod(i = 1, #p, if(isprime(primepi(p[i])), (p[i]^(e[i]+1)-1)/(p[i]-1), 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 A360328.
Cf. A076610.
Similar sequences: A006038, A091191, A249263, A302574, A360356.
Sequence in context: A116195 A249878 A360328 * A324897 A051259 A289517
KEYWORD
nonn
AUTHOR
Amiram Eldar, Feb 04 2023
STATUS
approved

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Last modified July 21 11:45 EDT 2024. Contains 374472 sequences. (Running on oeis4.)