cp's OEIS Frontend

A344694 Numbers k, not powers of primes, for which A011772(k) divides A344875(k), and for all proper divisors d of k, A011772(d) < A011772(k).

%I A344694 #7 Jun 05 2021 16:43:01
%S A344694 900,1260,1560,3740,6552,6669,9680,18981,19880,35784,36080,59040,
%T A344694 62238,62244,81872,103730,108500,118910,134420,160160,171740,185724,
%U A344694 211072,217833,222224,225929,227528,259325,351072,384944,404294,414778,422604,425178,446600,456228,463008,488205,490105,527100,574308,581184,598400
%N A344694 Numbers k, not powers of primes, for which A011772(k) divides A344875(k), and for all proper divisors d of k, A011772(d) < A011772(k).
%C A344694 Has many terms common with A344595.
%o A344694 (PARI)
%o A344694 A011772(n) = { if(n==1, return(1)); my(f=factor(if(n%2, n, 2*n)), step=vecmax(vector(#f~, i, f[i, 1]^f[i, 2]))); forstep(m=step, 2*n, step, if(m*(m-1)/2%n==0, return(m-1)); if(m*(m+1)/2%n==0, return(m))); }; \\ From A011772
%o A344694 A344875(n) = { my(f=factor(n)~); prod(i=1, #f, (f[1, i]^(f[2, i]+(2==f[1, i]))-1)); };
%o A344694 A344880(n) = { my(x=A011772(n)); fordiv(n, d, if(A011772(d)==x, return(d==n))); };
%o A344694 A344973(n) = (A344875(n)%A011772(n));
%o A344694 isA344694(n) = ((n>1)&&!isprimepower(n)&&(0==A344973(n))&&A344880(n));
%Y A344694 Cf. A011772, A344880, A344973.
%Y A344694 Intersection of A024619, A344881 and A344974. Intersection of A344881 and A344975.
%Y A344694 Cf. also A344595, A344980.
%K A344694 nonn
%O A344694 1,1
%A A344694 _Antti Karttunen_, Jun 05 2021