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

1, 2, 3, 6, 7, 9, 30, 31, 33, 37, 38, 39, 210, 211, 213, 217, 218, 219, 241, 242, 246, 247, 249, 2310, 2311, 2313, 2317, 2318, 2319, 2341, 2342, 2343, 2346, 2347, 2521, 2522, 2523, 2526, 2527, 2529, 2550, 2551, 2553, 2557, 2558, 2559, 30030, 30031, 30033, 30037, 30038, 30039, 30061, 30062, 30063, 30066, 30067, 30069, 30241

Offset: 1

Author

Antti Karttunen, Oct 30 2019

Keywords

• nonn

Comments

Numbers n such that A129251(n) = 0 and A328828(n) = 0 (or equally, A328114(n) = 1).

Terms k in A276156 for which A276086(A276085(k)) = k, i.e., those terms of A276156 which are in the range of A276086.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..23330
• Index entries for sequences related to primorial base

Crossrefs

Intersection of A048103 and A276156.

Cf. A002110, A129251, A276085, A276086, A328114, A328828, A328831, A328833, A328836.

Programs

PARI

A129251(n) = { my(f = factor(n)); sum(k=1, #f~, (f[k, 2]>=f[k, 1])); };
A328828(n) = { my(i=1, p=2); while(n, if((n%p)>1, return(i)); i++; n = n\p; p = nextprime(1+p)); (0); };
isA328832(n) = ((0==A129251(n)) && (0==A328828(n)));

PARI

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); };
k=0; for(n=1,(2^15)-1, if(!A129251(u=A276156(n)), k++; write("b328832.txt", k, " ", u, " ")));

Formula

a(n) = A276086(A328833(n)).