cp's OEIS Frontend

A328957 Numbers k such that sigma_0(k) != omega(k) * Omega(k), where sigma_0 = A000005, omega = A001221, Omega = A001222.

%I A328957 #19 Jul 28 2024 10:08:07
%S A328957 1,2,3,4,5,7,8,9,11,13,16,17,19,23,25,27,29,30,31,32,36,37,41,42,43,
%T A328957 47,49,53,59,61,64,66,67,70,71,72,73,78,79,81,83,89,97,100,101,102,
%U A328957 103,105,107,108,109,110,113,114,120,121,125,127,128,130,131,137
%N A328957 Numbers k such that sigma_0(k) != omega(k) * Omega(k), where sigma_0 = A000005, omega = A001221, Omega = A001222.
%H A328957 Amiram Eldar, <a href="/A328957/b328957.txt">Table of n, a(n) for n = 1..10000</a>
%F A328957 A000005(a(n)) != A001222(a(n)) * A001221(a(n)).
%e A328957 The sequence of terms together with their prime indices begins:
%e A328957     1: {}
%e A328957     2: {1}
%e A328957     3: {2}
%e A328957     4: {1,1}
%e A328957     5: {3}
%e A328957     7: {4}
%e A328957     8: {1,1,1}
%e A328957     9: {2,2}
%e A328957    11: {5}
%e A328957    13: {6}
%e A328957    16: {1,1,1,1}
%e A328957    17: {7}
%e A328957    19: {8}
%e A328957    23: {9}
%e A328957    25: {3,3}
%e A328957    27: {2,2,2}
%e A328957    29: {10}
%e A328957    30: {1,2,3}
%e A328957    31: {11}
%e A328957    32: {1,1,1,1,1}
%t A328957 Select[Range[100],DivisorSigma[0,#]!=PrimeOmega[#]*PrimeNu[#]&]
%o A328957 (PARI) is(k) = {my(f = factor(k)); numdiv(f) != omega(f) * bigomega(f);} \\ _Amiram Eldar_, Jul 28 2024
%Y A328957 Nonzeros of A328958.
%Y A328957 The complement is A328956.
%Y A328957 Prime signature is A124010.
%Y A328957 Omega-sequence is A323023.
%Y A328957 omega(n) * Omega(n) is A113901(n).
%Y A328957 (Omega(n) - 1) * omega(n) is A307409(n).
%Y A328957 sigma_0(n) - Omega(n) * omega(n) is A328958(n).
%Y A328957 sigma_0(n) - 2 - (Omega(n) - 1) * omega(n) is A328959(n).
%Y A328957 Cf. A060687, A070175, A090858, A112798, A303555, A320632, A328960, A328961, A328962, A328963, A328964, A328965.
%K A328957 nonn
%O A328957 1,2
%A A328957 _Gus Wiseman_, Nov 01 2019