cp's OEIS Frontend

A328832 Numbers that are sums of distinct primorial numbers, A002110, and do not have a factor of the form p^p.

%I A328832 #10 Nov 01 2019 18:39:17
%S A328832 1,2,3,6,7,9,30,31,33,37,38,39,210,211,213,217,218,219,241,242,246,
%T A328832 247,249,2310,2311,2313,2317,2318,2319,2341,2342,2343,2346,2347,2521,
%U A328832 2522,2523,2526,2527,2529,2550,2551,2553,2557,2558,2559,30030,30031,30033,30037,30038,30039,30061,30062,30063,30066,30067,30069,30241
%N A328832 Numbers that are sums of distinct primorial numbers, A002110, and do not have a factor of the form p^p.
%C A328832 Numbers n such that A129251(n) = 0 and A328828(n) = 0 (or equally, A328114(n) = 1).
%C A328832 Terms k in A276156 for which A276086(A276085(k)) = k, i.e., those terms of A276156 which are in the range of A276086.
%H A328832 Antti Karttunen, <a href="/A328832/b328832.txt">Table of n, a(n) for n = 1..23330</a>
%H A328832 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%F A328832 a(n) = A276086(A328833(n)).
%o A328832 (PARI)
%o A328832 A129251(n) = { my(f = factor(n)); sum(k=1, #f~, (f[k, 2]>=f[k, 1])); };
%o A328832 A328828(n) = { my(i=1, p=2); while(n, if((n%p)>1, return(i)); i++; n = n\p; p = nextprime(1+p)); (0); };
%o A328832 isA328832(n) = ((0==A129251(n)) && (0==A328828(n)));
%o A328832 (PARI)
%o A328832 A276156(n) = { my(p=2,pr=1,s=0); while(n,if(n%2,s += pr); n >>= 1; pr *= p; p = nextprime(1+p)); (s); };
%o A328832 k=0; for(n=1,(2^15)-1, if(!A129251(u=A276156(n)), k++; write("b328832.txt", k, " ", u, " ")));
%Y A328832 Intersection of A048103 and A276156.
%Y A328832 Cf. A002110, A129251, A276085, A276086, A328114, A328828, A328831, A328833, A328836.
%K A328832 nonn
%O A328832 1,2
%A A328832 _Antti Karttunen_, Oct 30 2019