A319715 - OEIS

%I #10 Mar 06 2024 01:00:34

%S 1,2,3,4,4,5,3,6,6,8,5,9,4,7,10,10,6,11,5,14,10,11,7,15,9,10,12,15,8,

%T 16,3,12,10,10,10,17,4,9,10,20,6,18,5,17,18,13,7,23,8,18,14,18,8,22,

%U 14,23,14,16,9,26,4,7,17,16,12,20,5,16,14,22,7,27,6,10,21,17,14,22,7,30,19,14,9,34,16,13,18,27,10,30,10,19,10

%N Sum of A276150(d) over divisors d of n, where A276150 gives the sum of digits in primorial base.

%C Inverse Möbius transform of A276150.

%H Antti Karttunen, <a href="/A319715/b319715.txt">Table of n, a(n) for n = 1..30030</a>

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

%F a(n) = Sum_{d|n} A276150(d).

%F a(n) = A319713(n) + A276150(n).

%t d[n_] := Module[{k = n, p = 2, s = 0, r}, While[{k, r} = QuotientRemainder[k, p]; k != 0 || r != 0, s += r; p = NextPrime[p]]; s]; a[n_] := DivisorSum[n, d[#] &]; Array[a, 100] (* _Amiram Eldar_, Mar 05 2024 *)

%o (PARI)

%o A276150(n) = { my(s=0, p=2, d); while(n, d = (n%p); s += d; n = (n-d)/p; p = nextprime(1+p)); (s); };

%o A319715(n) = sumdiv(n,d,A276150(d));

%Y Cf. A276150, A319712, A319713.

%K nonn,base

%O 1,2

%A _Antti Karttunen_, Oct 02 2018