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Antti Karttunen, <a href="/A129597/b129597.txt">Table of n, a(n) for n = 1..10000</a>
(PARI) A129597(n) = if(1==n, n, my(f=factor(n)); (2*n*n)/f[#f~, 1]); \\ Antti Karttunen, Oct 16 2021
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The sum of prime indices of a(n > 1) is 2*A056239(n) - A061395(n) + 1 for n > 1.
The odd version for odd indices is A342768(n) = a(n)/2 for n > 1.
A056239 A346633 adds up prime indices, row sums the even bisection of A112798standard compositions (odd: A209281).
A209281 (shifted) A346698 adds up the odd even bisection of standard compositionsprime indices (reverse: A346699).
A316524 gives the alternating sum of prime indices (reverse: A344616).
A346633 adds up the even bisection of standard compositions.
A346697 adds up the odd bisection of prime indices (reverse: A346699).
Cf. A000290, A000720, A006530, A037143, A341446, `A112798, A344606, A344617, `A344653, *A345957, `A345960, A346698, A346697, A346700, `A346701.
These are the positions of first appearances in A346704, and also in A329888.
A027193 counts partitions of odd length, ranked by A026424.
A103919 counts partitions by sum and alternating sum (reverse: A344612).
A344606 counts alternating permutations of prime indices.
A344617 gives the sign of the alternating sum of prime indices.
A346697 gives the sum of adds up the odd bisection of prime indices (reverse: A346699).
A346699 gives the sum of the odd bisection of reversed prime indices.
Cf. A000290, A000720, A006530, A033942, A037143, A341446, A344606, A344617, `A344653, *A345957, A345958, A345959, `A345960, A346635, A346698, A346700, `A346701, A346704.