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A336851
a(n) = sigma(A003961(n)) - A003961(n), where A003961 is a prime shift towards larger primes, sigma is the sum of divisors.
5
0, 1, 1, 4, 1, 9, 1, 13, 6, 11, 1, 33, 1, 15, 13, 40, 1, 49, 1, 41, 17, 17, 1, 105, 8, 21, 31, 57, 1, 87, 1, 121, 19, 23, 19, 178, 1, 27, 23, 131, 1, 123, 1, 65, 73, 33, 1, 321, 12, 81, 25, 81, 1, 249, 21, 183, 29, 35, 1, 309, 1, 41, 97, 364, 25, 141, 1, 89, 35, 153, 1, 565, 1, 45, 97, 105, 25, 177, 1, 401, 156, 47
OFFSET
1,4
COMMENTS
Even terms occur on square n, odd terms on nonsquare n.
Numbers k such that a(k) = 2^e for e >= 1, are: 4, 25, 841, 12769, 66896041, etc., i.e., terms of A073715 squared.
FORMULA
a(n) = A003973(n) - A003961(n) = A000203(A003961(n)) - A003961(n).
a(n) = A001065(A003961(n)).
a(n) = A336852(n) - A286385(n).
PROG
(PARI)
A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A336851(n) = (sigma(A003961(n)) - A003961(n));
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Aug 05 2020
EXTENSIONS
Comments edited by Antti Karttunen, Jul 03 2023
STATUS
approved