A353750 - OEIS

%I #24 Jan 26 2023 12:17:17

%S 1,4,2,30,4,8,4,48,132,24,8,60,30,16,16,870,24,528,24,120,16,48,16,96,

%T 870,120,48,120,48,96,16,720,32,144,32,3960,306,96,120,288,120,64,140,

%U 240,528,96,32,1740,1224,3480,96,1050,144,192,96,192,96,288,96,480,870,64,528,14238,240,192,416,720,64,192,96

%N a(n) = phi(sigma(n)) * A064989(sigma(n)), where A064989 shifts the prime factorization one step towards lower primes.

%C In contrast to A353749, this is not multiplicative, except on positions given by A336547.

%C It seems that a(n) = A353749(n) only on n=1. This would then imply that the intersection of A006872 and A336702 = {1}.

%H Antti Karttunen, <a href="/A353750/b353750.txt">Table of n, a(n) for n = 1..16384</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) = A353749(A000203(n)) = A062401(n) * A350073(n).

%F a(n) = A353749(n) + A353757(n).

%o (PARI)

%o A064989(n) = { my(f=factor(n>>valuation(n,2))); for(i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f); };

%o A353750(n) = { my(s=sigma(n)); (eulerphi(s)*A064989(s)); };

%Y Cf. A000010, A000203, A006872, A062401, A064989, A336547, A336548, A336549, A336702, A350073, A353747, A353748, A353749.

%Y Cf. A353757, A353758 (where a(n) < A353749(n)), A353759 (where a(n) >= A353749(n)), A353760, A353790 [= a(A003961(n))].

%Y Cf. also A353792.

%K nonn

%O 1,2

%A _Antti Karttunen_, May 07 2022

%E Dubious comment deleted by _Antti Karttunen_, Jan 26 2023