cp's OEIS Frontend

A340091 Odd numbers k such that A064989(k) is in A340151.

%I A340091 #12 Dec 31 2020 15:33:19
%S A340091 679,703,1387,1729,1891,2047,2509,2701,2821,3277,3367,5551,7471,7735,
%T A340091 8119,8827,9997,10963,11305,12403,13021,13747,13981,14491,14701,15841,
%U A340091 16471,17563,19951,21349,21907,21931,22015,23959,24727,25669,26281,27511,28939,29341,31417,32407,38503,39091,39831,39865,40501,41041
%N A340091 Odd numbers k such that A064989(k) is in A340151.
%C A340091 Sequence A003961(A340151(i)), for i >= 1, sorted into ascending order.
%C A340091 By definition, this has no common terms with A340077 nor any of its subsequences like A339869 or A339880.
%H A340091 Antti Karttunen, <a href="/A340091/b340091.txt">Table of n, a(n) for n = 1..3290</a>
%o A340091 (PARI)
%o A340091 A000265(n) = (n>>valuation(n,2));
%o A340091 A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
%o A340091 A339904(n) = A000265(eulerphi(A003961(n)));
%o A340091 A340075(n) = { my(u=A339904(n)); u/gcd(A003961(n)-1, u); };
%o A340091 A247074(n) = { my(f=factor(n)); eulerphi(f)/prod(i=1, #f~, gcd(f[i, 1]-1, n-1)); }; \\ From A247074
%o A340091 A340149(n) = A000265(A247074(A003961(n)));
%o A340091 isA340151(n) = ((1!=A340075(n))&&(1==A340149(n)));
%o A340091 A064989(n) = { my(f=factor(n)); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f) };
%o A340091 isA340091(n) = ((n%2)&&isA340151(A064989(n)));
%Y A340091 Cf. A002997, A003961, A339869, A339880, A340077, A340151.
%Y A340091 Cf. A340092 (Carmichael numbers in this sequence).
%K A340091 nonn
%O A340091 1,1
%A A340091 _Antti Karttunen_, Dec 31 2020