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A286385 a(n) = A003961(n) - A000203(n). 4
0, 0, 1, 2, 1, 3, 3, 12, 12, 3, 1, 17, 3, 9, 11, 50, 1, 36, 3, 21, 23, 3, 5, 75, 18, 9, 85, 43, 1, 33, 5, 180, 17, 3, 29, 134, 3, 9, 29, 99, 1, 69, 3, 33, 97, 15, 5, 281, 64, 54, 23, 55, 5, 255, 19, 177, 35, 3, 1, 147, 5, 15, 171, 602, 35, 51, 3, 45, 49, 87, 1, 480, 5, 9, 121, 67, 47, 87, 3, 381, 504, 3, 5, 271, 25, 9, 35, 171, 7, 291, 75, 93, 57, 15, 41, 963 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

All terms appear to be nonnegative? This question is equivalent to the question posed in A285705.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..16383

FORMULA

a(n) = A285705(A048673(n)) - 1 = 2*A048673(n) - A000203(n) - 1.

PROG

(PARI)

A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); }; \\ From Michel Marcus

A286385(n) = (A003961(n) - sigma(n));

for(n=1, 16384, write("b286385.txt", n, " ", A286385(n)));

(Scheme)

(define (A286385 n) (- (A003961 n) (A000203 n)))

(Python)

from sympy import factorint, nextprime, divisor_sigma as D

from operator import mul

def a048673(n):

    f = factorint(n)

    return 1 if n==1 else (1 + reduce(mul, [nextprime(i)**f[i] for i in f]))/2

def a(n): return 2*a048673(n) - D(n) - 1 # Indranil Ghosh, May 12 2017

CROSSREFS

Cf. A000203, A001359, A003961, A001065, A031924, A033879, A048673, A285705.

Sequence in context: A176054 A257703 A061413 * A074743 A181642 A011358

Adjacent sequences:  A286382 A286383 A286384 * A286386 A286387 A286388

KEYWORD

nonn

AUTHOR

Antti Karttunen, May 09 2017

STATUS

approved

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Last modified August 21 17:41 EDT 2017. Contains 290892 sequences.