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%I #20 Apr 30 2021 08:06:21
%S 0,1,2,3,6,5,8,9,24,11,14,13,30,17,32,33,120,35,38,25,54,27,44,43,144,
%T 47,62,49,150,65,152,153,720,155,158,73,174,63,92,79,264,81,98,71,198,
%U 87,188,187,840,191,206,109,294,111,212,199,864,215,302,217,870,305,872,873,5040,875,878,313,894,231,332,247,984,237,266,155,438,171
%N a(n) = A276075(A260443(n)).
%H Antti Karttunen, <a href="/A276081/b276081.txt">Table of n, a(n) for n = 0..8191</a>
%F a(n) = A276075(A260443(n)).
%o (Scheme)
%o (define (A276081 n) (A276075 (A260443 n)))
%o ;; A more practical standalone program, that uses memoization-macro definec:
%o (define (A276081 n) (sum_factorials_times_elements_in (A260443as_index_lists n)))
%o (definec (A260443as_index_lists n) (cond ((zero? n) (list)) ((= 1 n) (list 1)) ((even? n) (cons 0 (A260443as_index_lists (/ n 2)))) (else (add_two_lists (A260443as_index_lists (/ (- n 1) 2)) (A260443as_index_lists (/ (+ n 1) 2))))))
%o (define (add_two_lists nums1 nums2) (let ((len1 (length nums1)) (len2 (length nums2))) (cond ((< len1 len2) (add_two_lists nums2 nums1)) (else (map + nums1 (append nums2 (make-list (- len1 len2) 0)))))))
%o (define (sum_factorials_times_elements_in nums) (let loop ((s 0) (nums nums) (i 2) (f 1)) (cond ((null? nums) s) (else (loop (+ s (* (car nums) f)) (cdr nums) (+ 1 i) (* i f))))))
%o (Python)
%o from sympy import factorint, factorial as f, prime, primepi
%o from operator import mul
%o from functools import reduce
%o def a003961(n):
%o F=factorint(n)
%o return 1 if n==1 else reduce(mul, [prime(primepi(i) + 1)**F[i] for i in F])
%o def a260443(n): return n + 1 if n<2 else a003961(a260443(n//2)) if n%2==0 else a260443((n - 1)//2)*a260443((n + 1)//2)
%o def a276075(n):
%o F=factorint(n)
%o return 0 if n==1 else sum([F[i]*f(primepi(i)) for i in F])
%o def a(n): return a276075(a260443(n))
%o print([a(n) for n in range(101)]) # _Indranil Ghosh_, Jun 21 2017
%Y Cf. A000142, A002487, A260443, A276075.
%Y Cf. also A276080.
%K nonn,look
%O 0,3
%A _Antti Karttunen_, Aug 18 2016
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