cp's OEIS Frontend

A336548 Numbers k such that at least one pair sigma(p_i^e_i), sigma(p_j^e_j) [with i != j] share a prime factor, when k = p_1^e_1 * ... * p_h^e_h, where each p_i^e_i is the maximal power of prime p_i dividing k.

%I A336548 #50 May 11 2022 10:26:46
%S A336548 10,15,21,22,30,33,34,35,39,40,42,46,51,52,55,57,58,60,65,66,69,70,77,
%T A336548 78,82,84,85,87,88,90,91,93,94,95,98,102,105,106,110,111,114,115,118,
%U A336548 119,120,123,129,130,132,133,135,136,138,140,141,142,143,145,152,154,155,156,159,160,161,164,165,166,168,170
%N A336548 Numbers k such that at least one pair sigma(p_i^e_i), sigma(p_j^e_j) [with i != j] share a prime factor, when k = p_1^e_1 * ... * p_h^e_h, where each p_i^e_i is the maximal power of prime p_i dividing k.
%C A336548 Numbers k for which A353802(k) = Product_{p^e||k} A051027(p^e) > A051027(k), i.e. numbers at which points A051027 is not multiplicative. The notation p^e||k means that p^e divides k, but p^(1+e) does not.
%C A336548 If x is present, then also multiples y*x are present for all y for which gcd(x,y) = 1.
%C A336548 Also numbers at which points A062401 and A353750 are not multiplicative. - _Antti Karttunen_, May 09 2022
%H A336548 Antti Karttunen, <a href="/A336548/b336548.txt">Table of n, a(n) for n = 1..25000</a>
%F A336548 {k | A336562(k) > 0}. - _Antti Karttunen_, May 09 2022
%e A336548 10 = 2*5 is present as sigma(2) = 3 and sigma(5) = 6, and 3 and 6 share a prime factor (gcd(3,6) = 3). Also we see that sigma(sigma(2))*sigma(sigma(5)) = 4*12 = 48 > sigma(sigma(10)) = 39.
%o A336548 (PARI) isA336548(n) = !A336546(n);
%Y A336548 Cf. A051027, A062401, A336546, A336547 (complement), A336549, A353750, A353802.
%Y A336548 Cf. A336357, A336558, A336560, A336561, A353807 (subsequences).
%Y A336548 Positions of nonzero terms in A336562, in A353753 and in A353803.
%Y A336548 Positions of terms larger than 1 in A353755, in A353784 and in A353806.
%Y A336548 Subsequence of A024619.
%K A336548 nonn
%O A336548 1,1
%A A336548 _Antti Karttunen_, Jul 25 2020
%E A336548 The old definition moved to comments and replaced with a more generic, but equivalent definition by _Antti Karttunen_, May 09 2022