A353759 - OEIS

%I #10 May 11 2022 10:27:07

%S 1,2,4,6,8,9,10,12,16,18,20,24,25,28,30,32,36,40,44,45,48,49,50,52,54,

%T 56,60,64,68,72,74,75,76,80,81,84,88,90,96,98,100,104,108,112,116,117,

%U 120,121,126,128,132,136,140,144,148,150,152,156,160,162,164,168,172,176,180,192,196,198,200,204,208,216,220

%N Numbers k for which A353749(k) <= A353749(sigma(k)), where A353749(k) = phi(k) * A064989(k), and A064989 shifts the prime factorization one step towards lower primes.

%C If an odd number is in the intersection of A348749 and A353684, then it is certainly included in this sequence also.

%H <a href="/index/O#opnseqs">Index entries for sequences where odd perfect numbers must occur, if they exist at all</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>

%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 A353749(n) = (eulerphi(n)*A064989(n));

%o A353760(n) = { my(s=sigma(n)); (A353749(s)<A353749(n)); };

%o isA353759(n) = !A353760(n);

%Y Positions of nonnegative terms in A353757. Positions of 0's in A353760.

%Y Cf. A353749, A353750, A353758 (complement).

%Y Cf. A007691, A353764 (subsequences).

%Y Cf. also A348749, A353684, A353685.

%K nonn

%O 1,2

%A _Antti Karttunen_, May 10 2022