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A260442
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Sequence A260443 sorted into ascending order.
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8
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1, 2, 3, 5, 6, 7, 11, 13, 15, 17, 18, 19, 23, 29, 30, 31, 35, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 75, 77, 79, 83, 89, 90, 97, 101, 103, 105, 107, 109, 113, 127, 131, 137, 139, 143, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 210, 211, 221, 223, 227, 229, 233, 239, 241, 245, 251, 257, 263, 269, 270, 271, 277, 281, 283, 293, 307, 311
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OFFSET
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0,2
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COMMENTS
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Each term is a prime factorization encoding of one of the Stern polynomials. See A260443 for details.
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LINKS
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PROG
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(PARI)
allocatemem(2^30);
A048675(n) = my(f = factor(n)); sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2; \\ Michel Marcus, Oct 10 2016
A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From Michel Marcus
i=0; n=0; while(i < 10001, n++; if(isA260442(n), write("b260442.txt", i, " ", n); i++));
(Scheme, with Antti Karttunen's IntSeq-library)
;; An optimized version:
(Python)
from sympy import factorint, prime, primepi
from operator import mul
from functools import reduce
def a048675(n):
F=factorint(n)
return 0 if n==1 else sum([F[i]*2**(primepi(i) - 1) for i in F])
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 a(n): return n + 1 if n<2 else a003961(a(n//2)) if n%2==0 else a((n - 1)//2)*a((n + 1)//2)
print([n for n in range(301) if a(a048675(n))==n]) # Indranil Ghosh, Jun 21 2017
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CROSSREFS
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From 2 onward the positions of nonzeros in A277333.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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