cp's OEIS Frontend

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

%I A360355 #7 Feb 04 2023 20:56:51
%S A360355 7425,8415,46035,76725,101475,182655,355725,669735,1411425,1606275,
%T A360355 2352375,2891295,3592215,3650625,4079295,4861575,5053455,5870205,
%U A360355 6093225,6636465,6920595,7732395,8750835,9120375,9783675,9850005,9958905,10155375,11298375,11532375,12120075
%N A360355 Primitive terms of A360328: terms of A360328 with no proper divisor in A360328.
%C A360355 If m is a term then k*m is a term of A360328 for all k in A076610.
%C A360355 Analogous to primitive abundant numbers (A091191) with divisors that are restricted to numbers that have only prime-indexed prime factors.
%t A360355 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]
%o A360355 (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;}
%o A360355 is(n) = {if(!isab(n), return(0)); fordiv(n, d, if(d < n && isab(d), return(0))); return(1)};
%Y A360355 Subsequence of A360328.
%Y A360355 Cf. A076610.
%Y A360355 Similar sequences: A006038, A091191, A249263, A302574, A360356.
%K A360355 nonn
%O A360355 1,1
%A A360355 _Amiram Eldar_, Feb 04 2023