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Also, 70th powers of primes.

More generally, the n-th number with p divisors is equal to the n-th prime raised to power p-1, where p is prime. In this case, p = 71.

Also, 72nd powers of primes.

More generally, the n-th number with p divisors is equal to the n-th prime raised to power p-1, where p is prime. In this case, p = 73.

Since for numbers m^2 in the sequence the width at the diagonal of SRS(m^2) is 1, the area m of its center part is odd so that this sequence is a proper subsequence of A016754 and since SRS(m^2) has an odd number of parts it is a proper subsequence of A319529. The smallest odd square not in this sequence is 225 = 15^2. SRS(225) is {113, 177, 113}, its center part has maximum width 2, its width at the diagonal is 1.

The k+1 parts of SRS(p^(2k)), p an odd prime and k >= 0, through the diagonal including the center part have areas (p^(2k-i) + p^i)/2 for 0 <= i <= k. They form a strictly decreasing sequence. Since p^(2k) has 2k+1 divisors and SRS(p^(2k)) has 2k+1 parts, all of width 1 (A357581), the even powers of odd primes form a proper subsequence of A244579. For the subsequence of squares of odd primes p, SRS(p^2) consists of the 3 parts { (p^2 + 1)/2, p, (p^2 + 1)/2 } see A001248, A247687 and A357581.

The areas of the parts of SRS(m^2) need not be in descending order through the diagonal as a(112) = 275^2 = 75625 with SRS(75625) = (37813, 7565, 3443, 1525, 715, 738, 275, 738, 715, 1525, 3443, 7565, 37813) demonstrates.

An equivalent description of the sequence is: The center part of SRS(m^2) has width 1, m is odd, and A249223(m^2, m-1) = 0.

Conjectures (true for all a(n) <= 10^8):

(1) The central part of SRS(a(n)) is the minimum of all parts of SRS(a(n)), 1 <= n.

(2) The terms in this sequence are the squares of the terms in A244579.

A subsequence of A175745 (Numbers with 35 divisors).

First different term in A175745 is 17179869184(=2^34).

Number of elements in the set {(x, y): x|n, y|n, x < y, gcd(x, y) > 1}.

Every element of the sequence is repeated indefinitely, for instance:

a(n)=0 if n prime;

a(n)=1 if n = p^2 for p prime (A001248);

a(n)=2 if n is a squarefree semiprime (A006881);

a(n)=3 if n = p^3 for p prime (A030078);

a(n)=6 if n = p^4 for p prime (A030514);

a(n)=8 if n is a number which is the product of a prime and the square of a different prime (A054753);

a(n)=10 if n = p^5 for p prime (A050997);

a(n)=15 if n is in the set {A007304} union {64} = {30, 42, 64, 66, 70,...} = {Sphenic numbers} union {64};

a(n)=18 if n is the product of the cube of a prime (A030078) and a different prime (see A065036);

a(n)=21 if n = p^7 for p prime (A092759);

a(n)=24 if n is square of a squarefree semiprime (A085986);

a(n)=32 if n is the product of the 4th power of a prime (A030514) and a different prime (see A178739);

a(n)=36 if n = p^9 for p prime (A179665);

a(n)=44 if n is the product of exactly four primes, three of which are distinct (A085987);

a(n)=45 if n is a number with 11 divisors (A030629);

a(n)=49 if n is of the form p^2*q^3, where p,q are distinct primes (A143610);

a(n)=50 if n is the product of the 5th power of a prime (A050997) and a different prime (see A178740);

a(n)=55 if n if n = p^11 for p prime(A079395);

a(n)=72 if n is a number with 14 divisors (A030632);

a(n)=80 if n is the product of four distinct primes (A046386);

a(n)=83 if n is a number with 15 divisors (A030633);

a(n)=89 if n is a number with prime factorization pqr^3 (A189975);

a(n)=96 if n is a number that are the cube of a product of two distinct primes (A162142);

a(n)=98 if n is the product of the 7th power of a prime and a distinct prime (p^7*q) (A179664);

a(n)=116 if n is the product of exactly 2 distinct squares of primes and a different prime (p^2*q^2*r) (A179643);

a(n)=126 if n is the product of the 5th power of a prime and different distinct prime of the 2nd power (p^5*q^2) (A179646);

a(n)=128 if n is the product of the 8th power of a prime and a distinct prime (p^8*q) (A179668);

a(n)=150 if n is the product of the 4th power of a prime and 2 different distinct primes (p^4*q*r) (A179644);

a(n)=159 if n is the product of the 4th power of a prime and a distinct prime of power 3 (p^4*q^3) (A179666).

It is possible to continue with a(n) = 162, 178, 209, 224, 227, 238, 239, 260, 289, 309, 320, 333,...

Each of the following sequences, p^(q-1) with p >= 2 and q > 2 primes, except their respective first elements, powers of 2, is a subsequence:

A001248(p) = p^2, A030514(p) = p^4, A030516(p) = p^6,

A030629(p) = p^10, A030631(p) = p^12, A030635(p) = p^16,

A030637(p) = p^18, A137486(p) = p^22, A137492(p) = p^28,

A139571(p) = p^30, A139572(p) = p^36, A139573(p) = p^40,

A139574(p) = p^42, A139575(p) = p^46, A173533(p) = p^52,

A183062(p) = p^58, A183085(p) = p^60.

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The sequences A053182(n)^2, A065509(n)^4, A163268(n)^6 and A240693(n)^10 are subsequences of this sequence.

The odd numbers in A023194 are a subsequence of this sequence.

Also, 78th powers of primes.

More generally, the n-th number with p divisors is equal to the n-th prime raised to power p-1, where p is prime. In this case, p = 79.

Also, 82nd powers of primes.

More generally, the n-th number with p divisors is equal to the n-th prime raised to power p-1, where p is prime. In this case, p = 83.

Also, 88th powers of primes.

More generally, the n-th number with p divisors is equal to the n-th prime raised to power p-1, where p is prime. In this case, p = 89.

First differs from A374590 and A375432 at n = 25: A374590(25) = A375432(25) = 216 is not a term of this sequence.

Numbers k such that A382291(k) = 2, i.e., numbers whose number of infinitary divisors is twice the number of their unitary divisors.

Numbers whose prime factorization has a single exponent that is a sum of two distinct powers of 2 (A018900) and all the other exponents, if they exist, are powers of 2. Equivalently, numbers of the form p^e * m, where p is a prime, e is a term in A018900, and m is a term in A138302 that is coprime to p.

If k is a term then k^2 is also a term. If m is a term in A138302 that is coprime to k then k * m is also a term. The primitive terms, i.e., the terms that cannot be generated from smaller terms using these rules, are the numbers of the form p^(2^i+1), where p is prime and i >= 1.

Analogous to A060687, which is the sequence of numbers k with prime excess A046660(k) = 2.

The asymptotic density of this sequence is A271727 * Sum_{p prime} (((1 - 1/p)/f(1/p)) * Sum_{k>=1} 1/p^A018900(k)) = 0.11919967112489084407..., where f(x) = 1 - x^3 + Sum_{k>=2} (x^(2^k)-x^(2^k+1)).