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A328832
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Numbers that are sums of distinct primorial numbers, A002110, and do not have a factor of the form p^p.
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4
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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
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OFFSET
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1,2
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COMMENTS
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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.
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LINKS
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Antti Karttunen, Table of n, a(n) for n = 1..23330
Index entries for sequences related to primorial base
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FORMULA
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a(n) = A276086(A328833(n)).
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PROG
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(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, " ")));
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CROSSREFS
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Intersection of A048103 and A276156.
Cf. A002110, A129251, A276085, A276086, A328114, A328828, A328831, A328833, A328836.
Sequence in context: A018295 A033495 A006877 * A263881 A208892 A085397
Adjacent sequences: A328829 A328830 A328831 * A328833 A328834 A328835
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KEYWORD
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nonn
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AUTHOR
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Antti Karttunen, Oct 30 2019
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STATUS
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approved
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