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A057949 Numbers with more than one factorization into S-primes. See A054520 and A057948 for definition. 6
441, 693, 1089, 1197, 1449, 1617, 1881, 1953, 2205, 2277, 2541, 2709, 2793, 2961, 3069, 3249, 3381, 3465, 3717, 3933, 3969, 4221, 4257, 4389, 4473, 4557, 4653, 4761, 4977, 5229, 5301, 5313, 5445, 5733, 5841, 5929, 5985, 6237, 6321, 6417, 6489, 6633 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Numbers with k >= 4 prime factors (with multiplicity) that are congruent to 3 mod 4, no k-1 of which are equal. - Charlie Neder, Nov 03 2018

LINKS

Eric M. Schmidt, Table of n, a(n) for n = 1..10000

EXAMPLE

2205 is in S = {1,5,9, ... 4i+1, ...}, 2205 = 5*9*49 = 5*21^2; 5, 9, 21 and 49 are S-primes (A057948).

PROG

(Sage)

def A057949_list(bound) :

    numterms = (bound-1)//4 + 1

    M = [1] * numterms

    for k in range(1, numterms) :

        if M[k] == 1 :

            kpower = k

            while kpower < numterms :

                step = 4*kpower+1

                for j in range(kpower, numterms, step) :

                    M[j] *= 4*k+1

                kpower = 4*kpower*k + kpower + k

    # Now M[k] contains the product of the terms p^e where p is an S-prime

    # and e is maximal such that p^e divides 4*k+1

    return [4*k+1 for k in range(numterms) if M[k] > 4*k+1]

# Eric M. Schmidt, Dec 11 2016

(PARI) ok(n)={if(n%4==1, my(f=factor(n)); my(s=[f[i, 2] | i<-[1..#f~], f[i, 1]%4==3]); vecsum(s)>=4 && vecmax(s)<vecsum(s)-1, 0)} \\ Andrew Howroyd, Nov 25 2018

CROSSREFS

Cf. A054520, A057948, A057950.

Sequence in context: A207045 A252201 A252194 * A057950 A250808 A202400

Adjacent sequences:  A057946 A057947 A057948 * A057950 A057951 A057952

KEYWORD

nonn

AUTHOR

Jud McCranie, Oct 14 2000

EXTENSIONS

Offset corrected by Eric M. Schmidt, Dec 11 2016

STATUS

approved

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Last modified May 26 08:39 EDT 2020. Contains 334620 sequences. (Running on oeis4.)