A360356 -id:A360356 - cp's OEIS frontend

A360355 Primitive terms of A360328: terms of A360328 with no proper divisor in A360328.

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

Offset: 1

Amiram Eldar, Feb 04 2023

nonn

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.

Subsequence of A360328.
Cf. A076610.
Similar sequences: A006038, A091191, A249263, A302574, A360356.

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]

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)};

cp's OEIS Frontend

A360355 Primitive terms of A360328: terms of A360328 with no proper divisor in A360328.

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