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A337542
Number of proper divisors d of n for which sigma(A003961(d)) >= 2*sigma(d), where sigma is the sum of divisors, and A003961(x) shifts the prime factorization of x one step towards larger primes.
4
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 3, 0, 0, 1, 1, 0, 2, 0, 2, 0, 0, 0, 4, 0, 0, 0, 2, 0, 3, 0, 0, 2, 0, 0, 5, 0, 0, 0, 0, 0, 4, 0, 3, 0, 0, 0, 5, 0, 0, 2, 3, 0, 1, 0, 0, 0, 2, 0, 7, 0, 0, 1, 0, 0, 1, 0, 4, 2, 0, 0, 6, 0, 0, 0, 2, 0, 6, 0, 0, 0, 0, 0, 7, 0, 2, 1, 2, 0, 1, 0, 2, 3
OFFSET
1,18
COMMENTS
Number of terms of A337381 less than n that divide n.
FORMULA
a(n) = Sum_{d|n, d<n} A337383(d).
a(n) = A337541(n) - A337383(n).
PROG
(PARI)
A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A337542(n) = sumdiv(n, d, (d<n)&&sigma(A003961(d))>=2*sigma(d));
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Aug 31 2020
STATUS
approved