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 A329349 Number of occurrences of the largest primorial present in the greedy sum of primorials adding to A108951(n). 5
 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 4, 1, 2, 6, 2, 1, 2, 1, 4, 6, 2, 1, 1, 4, 2, 1, 4, 1, 1, 1, 1, 6, 2, 2, 4, 1, 2, 6, 1, 1, 1, 1, 4, 5, 2, 1, 3, 1, 8, 6, 4, 1, 2, 2, 8, 6, 2, 1, 3, 1, 2, 3, 2, 1, 12, 1, 4, 6, 5, 1, 1, 1, 2, 2, 4, 16, 12, 1, 2, 6, 2, 1, 2, 1, 2, 6, 8, 1, 10, 12, 4, 6, 2, 1, 6, 1, 2, 2, 1, 1, 12, 1, 8, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS The greedy sum is also the sum with the minimal number of primorials, used for example in the primorial base representation. LINKS Antti Karttunen, Table of n, a(n) for n = 1..10000 Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537 FORMULA a(n) = A276153(A108951(n)) = A071178(A324886(n)). a(n) <= A324888(n). EXAMPLE For n = 21 = 3 * 7, A108951(21) = A034386(3) * A034386(7) = 6 * 210, so the factor of the largest primorial present (210) in the greedy sum is 6 (as 1260 = 210 + 210 + 210 + 210 + 210 + 210), thus a(21) = 6. 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 largest primorial in the sum is 1, we have a(24) = 1. PROG (PARI) A034386(n) = prod(i=1, primepi(n), prime(i)); A108951(n) = { my(f=factor(n)); prod(i=1, #f~, A034386(f[i, 1])^f[i, 2]) };  \\ From A108951 A276153(n) = { my(e=0, p=2); while(n, e=n%p; n = n\p; p = nextprime(1+p)); (e); }; A329349(n) = A276153(A108951(n)); (PARI) A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); }; A324886(n) = A276086(A108951(n)); A071178(n) = if(1==n, 0, my(es=factor(n)[, 2]); es[#es]); A329349(n) = A071178(A324886(n)); CROSSREFS Cf. A002110, A034386, A071178, A108951, A276086, A276153, A324886, A324888, A329040, A329343, A329344, A329345, A329348. Sequence in context: A025903 A175327 A101211 * A329348 A329344 A081652 Adjacent sequences:  A329346 A329347 A329348 * A329350 A329351 A329352 KEYWORD nonn AUTHOR Antti Karttunen, Nov 11 2019 STATUS approved

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Last modified June 24 00:10 EDT 2021. Contains 345403 sequences. (Running on oeis4.)