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A319715 Sum of A276150(d) over divisors d of n, where A276150 gives the sum of digits in primorial base.

%I A319715 #10 Mar 06 2024 01:00:34
%S A319715 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 A319715 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 A319715 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 A319715 Sum of A276150(d) over divisors d of n, where A276150 gives the sum of digits in primorial base.
%C A319715 Inverse Möbius transform of A276150.
%H A319715 Antti Karttunen, <a href="/A319715/b319715.txt">Table of n, a(n) for n = 1..30030</a>
%H A319715 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>.
%F A319715 a(n) = Sum_{d|n} A276150(d).
%F A319715 a(n) = A319713(n) + A276150(n).
%t A319715 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 A319715 (PARI)
%o A319715 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 A319715(n) = sumdiv(n,d,A276150(d));
%Y A319715 Cf. A276150, A319712, A319713.
%K A319715 nonn,base
%O A319715 1,2
%A A319715 _Antti Karttunen_, Oct 02 2018