cp's OEIS Frontend

A351553 Even numbers k such that there are no odd prime factors p of sigma(k) such that p does not divide A003961(k) and the valuation(k, p) is different from valuation(sigma(k), p), where A003961 is fully multiplicative with a(p) = nextprime(p), and sigma is the sum of divisors function.

%I A351553 #22 Aug 27 2025 18:22:21
%S A351553 2,6,10,14,20,22,24,28,30,34,40,42,46,54,60,62,66,70,84,94,102,106,
%T A351553 110,114,120,130,138,140,142,154,160,168,170,174,182,186,190,198,210,
%U A351553 214,216,220,224,230,238,254,260,264,270,280,282,290,308,310,318,322,330,340,354,374,378,380,382,390,408,410,420,426
%N A351553 Even numbers k such that there are no odd prime factors p of sigma(k) such that p does not divide A003961(k) and the valuation(k, p) is different from valuation(sigma(k), p), where A003961 is fully multiplicative with a(p) = nextprime(p), and sigma is the sum of divisors function.
%C A351553 Even numbers k for which A351555(k) = 0.
%H A351553 Antti Karttunen, <a href="/A351553/b351553.txt">Table of n, a(n) for n = 1..10000</a>
%H A351553 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A351553 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%o A351553 (PARI)
%o A351553 A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); }; A351555(n) = { my(s=sigma(n),f=factor(s),u=A003961(n)); sum(k=1,#f~,if((f[k,1]%2) && 0!=(u%f[k,1]), (valuation(n,f[k,1])!=f[k,2]), 0)); };
%o A351553 isA351553(n) = (!(n%2) && 0==A351555(n));
%Y A351553 Cf. A000203, A005820, A003961, A046060, A351552.
%Y A351553 Even terms in A351554, positions of zeros at even indices in A351555.
%Y A351553 Cf. A351543 (complement among even numbers), A386430.
%K A351553 nonn,changed
%O A351553 1,1
%A A351553 _Antti Karttunen_, Feb 16 2022
%E A351553 Definition corrected by _Antti Karttunen_, Aug 27 2025