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A348950 a(n) = A348507(A276086(n)), where A348507(n) = A003959(n) - n, A003959 is multiplicative with a(p^e) = (p+1)^e, and A276086 gives the prime product form of primorial base expansion of n.

%I A348950 #14 Nov 14 2021 01:26:56
%S A348950 0,1,1,6,7,30,1,8,9,42,51,198,11,58,69,282,351,1278,91,398,489,1842,
%T A348950 2331,8118,671,2638,3309,11802,15111,50958,1,10,11,54,65,258,13,74,87,
%U A348950 366,453,1674,113,514,627,2406,3033,10674,853,3434,4287,15486,19773,67194,5993,22354,28347,98166,126513,418914,15,94,109
%N A348950 a(n) = A348507(A276086(n)), where A348507(n) = A003959(n) - n, A003959 is multiplicative with a(p^e) = (p+1)^e, and A276086 gives the prime product form of primorial base expansion of n.
%H A348950 Antti Karttunen, <a href="/A348950/b348950.txt">Table of n, a(n) for n = 0..11550</a>
%H A348950 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%F A348950 a(n) = A348949(n) - A276086(n) = A348507(A276086(n)).
%o A348950 (PARI)
%o A348950 A003959(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1]++); factorback(f); };
%o A348950 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A348950 A348507(n) = (A003959(n) - n);
%o A348950 A348950(n) = A348507(A276086(n));
%o A348950 (PARI) A348950(n) = { my(m1=1, m2=1, p=2); while(n, m1 *= (p^(n%p)); m2 *= ((1+p)^(n%p)); n = n\p; p = nextprime(1+p)); (m2-m1); };
%Y A348950 Cf. A003959, A276086, A348507, A348949, A348999.
%Y A348950 Cf. also A327860.
%K A348950 nonn,base
%O A348950 0,4
%A A348950 _Antti Karttunen_, Nov 06 2021