A329348 - OEIS

%I #32 Jan 17 2020 23:37:24

%S 1,1,1,2,1,2,1,1,1,2,1,4,1,2,6,2,1,2,1,4,6,2,1,3,2,2,1,4,1,5,1,1,6,2,

%T 8,4,1,2,6,1,1,1,1,4,1,2,1,1,1,4,6,4,1,2,4,8,6,2,1,3,1,2,3,2,13,12,1,

%U 4,6,5,1,3,1,2,5,4,2,12,1,2,1,2,1,2,11,2,6,8,1,2,6,4,6,2,7,2,1,2,10,1,1,12,1,8,4

%N The least significant nonzero digit in the primorial base expansion of primorial inflation of n, A108951(n).

%C Number of occurrences of the least primorial present in the greedy sum of primorials adding to A108951(n).

%C The greedy sum is also the sum with the minimal number of primorials, used for example in the primorial base representation.

%H Antti Karttunen, <a href="/A329348/b329348.txt">Table of n, a(n) for n = 1..65537</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

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

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

%F a(n) = A067029(A324886(n)) = A276088(A108951(n)).

%F a(n) <= A324888(n).

%F From _Antti Karttunen_, Jan 15-17 2020: (Start)

%F a(n) = A331188(n) mod A117366(n).

%F a(n) = A001511(A246277(A324886(n))).

%F (End)

%e For n = 24 = 2^3 * 3, A108951(24) = A034386(2)^3 * A034386(3) = 2^3 * 6 = 48 = 1*30 + 3*6, and as the factor of the least primorial in the sum is 3, we have a(24) = 3.

%o (PARI)

%o A034386(n) = prod(i=1, primepi(n), prime(i));

%o A108951(n) = { my(f=factor(n)); prod(i=1, #f~, A034386(f[i, 1])^f[i, 2]) };  \\ From A108951

%o A276088(n) = { my(e=0, p=2); while(n && !(e=(n%p)), n = n/p; p = nextprime(1+p)); (e); };

%o A329348(n) = A276088(A108951(n));

%o (PARI)

%o A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };

%o A324886(n) = A276086(A108951(n));

%o A067029(n) = if(1==n, 0, factor(n)[1, 2]); \\ From A067029

%o A329348(n) = A067029(A324886(n));

%o (PARI)

%o A002110(n) = prod(i=1, n, prime(i));

%o A329348(n) = if(1==n, n, my(f=factor(n), p=nextprime(1+vecmax(f[, 1]))); prod(i=1, #f~, A002110(primepi(f[i, 1]))^(f[i, 2]-(#f~==i)))%p); \\ _Antti Karttunen_, Jan 15 2020

%Y Cf. A002110, A034386, A067029, A108951, A117366, A276086, A276088, A324886, A324888, A329040, A329345, A329343, A329344, A329349, A331188, A331289, A331290, A331291.

%Y Cf. also A331292 (the next digit to left of this one), A331293.

%K nonn

%O 1,4

%A _Antti Karttunen_, Nov 11 2019

%E Name changed by _Antti Karttunen_, Jan 17 2020