A276081 a(n) = A276075(A260443(n)).

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, 47, 62, 49, 150, 65, 152, 153, 720, 155, 158, 73, 174, 63, 92, 79, 264, 81, 98, 71, 198, 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

Offset: 0

Author

Antti Karttunen, Aug 18 2016

Keywords

• nonn
• look

Links

• Antti Karttunen, Table of n, a(n) for n = 0..8191

Crossrefs

Cf. A000142, A002487, A260443, A276075.

Cf. also A276080.

Programs

Python

from sympy import factorint, factorial as f, prime, primepi
from operator import mul
from functools import reduce
def a003961(n):
    F=factorint(n)
    return 1 if n==1 else reduce(mul, [prime(primepi(i) + 1)**F[i] for i in F])
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)
def a276075(n):
    F=factorint(n)
    return 0 if n==1 else sum([F[i]*f(primepi(i)) for i in F])
def a(n): return a276075(a260443(n))
print([a(n) for n in range(101)]) # Indranil Ghosh, Jun 21 2017

Scheme

(define (A276081 n) (A276075 (A260443 n)))
;; A more practical standalone program, that uses memoization-macro definec:
(define (A276081 n) (sum_factorials_times_elements_in (A260443as_index_lists n)))
(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))))))
(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)))))))
(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))))))

Formula

a(n) = A276075(A260443(n)).