A351547 - OEIS

%I #13 Jul 09 2022 18:31:37

%S 1,1,4,7,6,4,8,15,13,2,12,28,14,8,24,31,18,13,20,6,32,4,24,12,31,14,

%T 40,56,30,8,32,63,48,2,48,91,38,20,56,90,42,32,44,84,78,8,48,124,57,

%U 31,72,98,54,40,72,120,16,10,60,24,62,32,104,127,12,16,68,14,96,16,72,195,74,38,124,140,96,56,80,186,121

%N a(n) = sigma(n) / A351545(n).

%H Antti Karttunen, <a href="/A351547/b351547.txt">Table of n, a(n) for n = 1..20000</a>

%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>

%F a(n) = A000203(n) / A351545(n).

%F a(n) = A351546(n) * A354997(n). - _Antti Karttunen_, Jul 09 2022

%o (PARI)

%o A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };

%o A351547(n) = { my(s=sigma(n),f=factor(s),u=A003961(n)); s/prod(k=1,#f~,if(!(u%f[k,1]) && (f[k,2]>=valuation(u,f[k,1])), f[k,1]^f[k,2], 1)); };

%Y Cf. A000203, A003961, A351545, A351546, A354997.

%Y Cf. A286385, A342671, A349161, A349162.

%K nonn

%O 1,3

%A _Antti Karttunen_, Feb 16 2022