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%I #17 Feb 17 2022 14:17:25
%S 2,6,10,14,20,22,24,28,30,34,40,42,46,54,60,62,66,70,84,94,102,106,
%T 110,114,120,130,138,140,142,154,160,168,170,174,182,186,190,198,210,
%U 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 Even numbers k such that there are no odd prime factors p of k such that p would not divide A003961(k) and the valuation(k, p) would be 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 Even numbers k for which A351555(k) = 0.
%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%o (PARI)
%o 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 isA351553(n) = (!(n%2) && 0==A351555(n));
%Y Cf. A000203, A005820, A003961, A046060, A351552.
%Y Even terms in A351554, positions of zeros at even indices in A351555.
%Y Cf. A351543 (complement among even numbers).
%K nonn
%O 1,1
%A _Antti Karttunen_, Feb 16 2022
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