

A324382


Minimal number of primorials that add to the nth highly composite number: a(n) = A276150(A002182(n)).


9



1, 1, 2, 1, 2, 4, 2, 4, 2, 4, 6, 2, 6, 6, 4, 6, 8, 2, 4, 6, 8, 12, 16, 20, 12, 14, 18, 12, 12, 12, 12, 12, 12, 12, 24, 8, 8, 8, 4, 16, 8, 16, 8, 16, 24, 16, 32, 6, 14, 30, 12, 18, 18, 24, 12, 18, 18, 24, 18, 36, 8, 14, 32, 28, 6, 24, 38, 12, 18, 36, 20, 24, 30, 40, 26, 10, 40, 20, 30, 18, 38, 26, 36, 36, 24, 24, 44, 50, 48, 14, 42
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OFFSET

1,3


COMMENTS

Among the first 10000 highly composite numbers, only in two cases a(n) < A112779(n). This happens on A002182(12) = 240 and A002182(18) = 2520. Note that A112779(n) gives the number of primorials needed when A002182(n) is expressed as a product [not as a sum] of primorials.


LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10000
Index entries for sequences related to primorial base
Index entries for sequences related to primorial numbers


FORMULA

a(n) = A276150(A002182(n)).
a(n) >= A324381(n).


EXAMPLE

For n=12, A002182(12) = 240, which is written as "11000" in primorial base (A049345) because 240 = 1*A002110(4) + 1*A002110(3) = 210+30, thus a(12) = 1+1 = 2. (Note that 240 = 30*2*2*2).
For n=18, A002182(18) = 2520 = "110000" in primorial base because 2520 = 1*A002110(5) + 1*A002110(4) = 2310+210, thus a(18) = 1+1 = 2. (Note that 2520 = 210*6*2).
For n=26, A002182(26) = 45360 = "1670000" in primorial base because 45360 = 1*A002110(6) + 6*A002110(5) + 7*A002110(4), thus a(26) = 1+6+7 = 14. (Note that 45360 = 210*6*6*6).


PROG

(PARI)
A276150(n) = { my(s=0, m); forprime(p=2, , if(!n, return(s)); m = n%p; s += m; n = (nm)/p); };
A324382(n) = A276150(A002182(n));


CROSSREFS

Cf. A002110, A002182, A276150, A324381.
Cf. also A108602, A112778, A112779, A324342.
Sequence in context: A300417 A121339 A307236 * A234359 A099500 A120253
Adjacent sequences: A324379 A324380 A324381 * A324383 A324384 A324385


KEYWORD

nonn


AUTHOR

Antti Karttunen, Feb 26 2019


STATUS

approved



