A376413 - OEIS

%I #10 Nov 14 2024 08:22:03

%S 0,1,2,6,3,30,4,7,210,2310,31,8,30030,5,510510,32,211,9699690,12,2311,

%T 223092870,9,6469693230,212,30031,36,200560490130,510511,2312,

%U 7420738134810,33,304250263527210,10,9699691,13082761331670030,60,13,30032,614889782588491410,216,510512,223092871,32589158477190044730

%N a(n) = A276085(A048103(n)), where A276085 is the primorial base log-function, and A048103 is the range of the primorial base exp-function (A276086).

%C Permutation of nonnegative integers.

%H Antti Karttunen, <a href="/A376413/b376413.txt">Table of n, a(n) for n = 1..1712</a>

%H <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

%F a(n) = A276085(A048103(n)).

%F For all n >= 1, A376411(a(n)) = n-1.

%o (PARI)

%o A276085(n) = { my(f = factor(n), pr=1, i=1, s=0); for(k=1, #f~, while(i <= primepi(f[k, 1])-1, pr *= prime(i); i++); s += f[k, 2]*pr); (s); };

%o A359550(n) = { my(pp); forprime(p=2, , pp = p^p; if(!(n%pp), return(0)); if(pp > n, return(1))); }; \\ _Antti Karttunen_, Nov 13 2024

%o for(n=1,105,if(A359550(n),print1(A276085(n),", ")));

%Y Cf. A048103, A276085, A276086.

%Y Cf. A376411 (inverse permutation, but note the different offsets and ranges).

%Y Cf. also A048672 (analogous permutation for base-2).

%K nonn

%O 1,3

%A _Antti Karttunen_, Nov 13 2024