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A319352 a(n) = Product_{d|n, d prime(1+A056239(d)), where A056239(d) gives the weight of the partition whose Heinz-number is d.

%I A319352 #9 Sep 17 2018 15:45:56
%S A319352 1,2,2,6,2,30,2,30,10,42,2,1050,2,66,70,210,2,2310,2,2310,110,78,2,
%T A319352 80850,14,102,110,4290,2,210210,2,2310,130,114,154,1651650,2,138,170,
%U A319352 210210,2,510510,2,6630,10010,174,2,11561550,22,7854,190,9690,2,510510,182,510510,230,186,2,2555102550,2,222,20570,30030,238,881790,2
%N A319352 a(n) = Product_{d|n, d<n} prime(1+A056239(d)), where A056239(d) gives the weight of the partition whose Heinz-number is d.
%H A319352 Antti Karttunen, <a href="/A319352/b319352.txt">Table of n, a(n) for n = 1..8192</a>
%F A319352 a(n) = Product_{d|n, d<n} prime(1+A056239(d)).
%F A319352 For all n >= 1:
%F A319352 A001221(a(n)) = A304793(n).
%F A319352 A001222(a(n)) = A032741(n).
%F A319352 1+A056169(a(n)) = A301855(n).
%o A319352 (PARI)
%o A319352 A056239(n) = { my(f); if(1==n, 0, f=factor(n); sum(i=1, #f~, f[i,2] * primepi(f[i,1]))); }
%o A319352 A319352(n) = { my(m=1); fordiv(n, d, if(d<n, m *= prime(1+A056239(d)))); (m); };
%Y A319352 Cf. A056239, A319353 (rgs-transform).
%K A319352 nonn
%O A319352 1,2
%A A319352 _Antti Karttunen_, Sep 17 2018