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A377868
a(n) = A359550(A276085(n)), where A359550 is multiplicative with a(p^e) = 1 if p > e, otherwise 0, and A276085 is fully additive with a(p) = p#/p.
8
0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0
OFFSET
1
COMMENTS
a(n) differs from A377874(n) = 1-A369001(n) for the first time at n=174, 232, 282, etc. See A377875.
FORMULA
a(n) <= A377874(n).
EXAMPLE
A276085(174) = 223092873 = 3^4 * 1063 * 2591, which has a divisor of the form p^e, with e >= p, thus a(174) = 0.
PROG
(PARI)
A276085(n) = { my(f = factor(n), pr=1, i=1, s=0); for(k=1, #f~, while(i <= primepi(f[k, 1])-1, pr *= prime(i); i++); s += f[k, 2]*pr); (s); };
A377868(n) = if(isprime(n), 1, my(x=A276085(n), pp); forprime(p=2, , pp = p^p; if(!(x%pp), return(0)); if(pp > x, return(1))));
(PARI)
A359550(n) = { my(pp); forprime(p=2, , pp = p^p; if(!(n%pp), return(0)); if(pp > n, return(1))); };
A377868(n) = if(1==n, 0, if(isprime(n), 1, my(f = factor(n), pr=1, i=1, s=0); if(2==vecsum(f[, 2]), return(2==f[1, 1]), for(k=1, #f~, while(i <= primepi(f[k, 1])-1, pr *= prime(i); i++); s += f[k, 2]*pr); A359550(s)))); \\ Antti Karttunen, Nov 17 2024
CROSSREFS
Characteristic function of A377869.
Differs from A377874 at the positions given by A377875.
Sequence in context: A022932 A334812 A079421 * A377874 A374128 A304438
KEYWORD
nonn
AUTHOR
Antti Karttunen, Nov 10 2024
STATUS
approved